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All the banality of the Webthe spelling and grammatical)Tj T* 0.0056 Tc (errors, the LOL cats, the Rickrollingbut also the collected works of Twain, Dickens,)Tj T* 0.0011 Tc -0.0011 Tw [(Austen,)-283.8(and millions of other authors.)]TJ 0 -2.2222 TD 0 Tc 0 Tw (The trillion-word data set was published by Thorsten Brants and Alex Franz of Google in)Tj 0 -1.4444 TD (2006 and is available through the Linguistic Data Consortium \()Tj /F6 1 Tf 28.0233 0 TD (http://tinyurl.com/ngrams)Tj /F2 1 Tf 10.45 0 TD (\).)Tj -38.4733 -1.4444 TD (The data set summarizes the original texts by)Tj /F6 1 Tf 20.2967 0 TD (counting)Tj /F2 1 Tf 3.4467 0 TD ( the number of appearances of each)Tj -23.7433 -1.4444 TD (word, and of each two-, three-, four-, and five-word sequence. For example, the)Tj T* (appears 23 billion times \(2.2% of the trillion words\), making it the most common word.)Tj T* (The word rebating appears 12,750 times \(a millionth of a percent\), as does fnuny)Tj T* 0.0071 Tc 0.0029 Tw [(\(apparently )10(a )10(misspelling)-270.6(of funny\). In three-word sequences, Find all posts appears)]TJ T* 0.01 Tc 0 Tw (13 million times \(.001%\), about as often as each of the, but well below the 100 mil-)Tj T* 0.0044 Tc -0.0044 Tw [(lion )-10(of )-10(All )-10(Rights )-10(Reserved )-10(\(.01%\).)-293.4(Heres an excerpt from the three-word sequences:)]TJ ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g 0 Tc 0 Tw (,ch14.14922 Page 219 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 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")Tj T* ( \012 #$% )Tj T* ( \012 &! ')Tj T* ( \012 % )Tj T* ( \012 )Tj T* ( \012 % )Tj T* ( \012 )Tj T* ( \012 \012\012% ")Tj T* ( \012 ')Tj T* ( \012 $$ )Tj T* ( \012 ')Tj /F2 1 Tf 9 0 0 9 126 511.75 Tm [(We)-257.8(see,)-258.5(for)-258.9(example,)-257.3(that)-258.5(Turks)-257.9(are)-258.8(the)-258.2(most)-258.4(outraged)-257.2(group)-259.1(\(on)-257.3(the)-259.3(Web,)-257.2(at)-259.2(the)-257.1(time)-258.8(the)]TJ 0 -1.4444 TD [(data)-271(was)-271.5(collected\),)-271.7(and)-271.9(that)-270.8(Republicans)-271.2(and)-271.9(liberals)-271(are)-272.1(outraged)-270.5(occasionally,)-272.1(but)-271.2(Dem-)]TJ T* (ocrats and conservatives dont make the list.)Tj 0 -2.2222 TD [(Why)-250.9(would)-251.8(I)-250.2(say)-251.8(this)-251.2(data)-251(is)-250.8(beautiful,)-251.2(and)-250.8(not)-251.1(merely)-251.3(mundane?)-250.7(Each)-251.8(individual)-251.4(count)]TJ /F6 1 Tf 39.1367 0 TD (is)Tj /F2 1 Tf -39.1367 -1.4444 TD (mundane. But the)Tj /F6 1 Tf 8.4444 0 TD (aggregation)Tj /F2 1 Tf 4.6656 0 TD ( of the countsbillions of countsis beautiful, because it)Tj -13.11 -1.4444 TD (says so much, not just about the English language, but about the world that speakers)Tj T* (inhabit. The data is beautiful because it represents much of what is worth saying.)Tj 0 -2.2222 TD (Before seeing what we can do with the data, we need to talk the talklearn a little bit of)Tj 0 -1.4444 TD (jargon. A collection of text is called a)Tj /F6 1 Tf 16.6522 0 TD (corpus)Tj /F2 1 Tf 2.5567 0 TD (. We treat the corpus as a sequence of)Tj /F6 1 Tf 17.0956 0 TD (tokens)Tj /F2 1 Tf 2.5 0 TD ()Tj -38.8044 -1.4444 TD (words and punctuation. Each distinct token is called a)Tj /F6 1 Tf 24.2633 0 TD (type)Tj /F2 1 Tf 1.6111 0 TD (, so the text Run, Lola Run)Tj -25.8744 -1.4444 TD (has four tokens \(the comma counts as one\) but only three types. 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Most of the)Tj T* (types are rare, however; the 10 most common types cover almost 1/3 of the tokens, the)Tj T* (top 1,000 cover just over 2/3, and the top 100,000 cover 98%.)Tj 0 -2.2222 TD [(A)-242.4(1-token)-243.4(sequence)-242.3(is)-243(a)]TJ /F6 1 Tf 10.7144 0 TD (unigram)Tj /F2 1 Tf 3.5011 0 TD [(,)-243.1(a)-242.2(2-token)-243.4(sequence)-242.3(is)-243(a)]TJ /F6 1 Tf 11.0133 0 TD (bigram)Tj /F2 1 Tf 2.8889 0 TD [(,)-243.1(and)-243(an)]TJ /F6 1 Tf 3.7844 0 TD (n)Tj /F2 1 Tf 0.5567 0 TD [(-token)-242.8(sequence)]TJ -32.4589 -1.4444 TD (is an)Tj /F6 1 Tf 2.3344 0 TD (n-gram)Tj /F2 1 Tf 3 0 TD (. P stands for)Tj /F6 1 Tf 5.9833 0 TD (probability)Tj /F2 1 Tf 4.3889 0 TD (, as in P\()Tj /F6 1 Tf 3.8356 0 TD (the)Tj /F2 1 Tf 1.2233 0 TD (\) = .022, which means that the probability)Tj -20.7656 -1.4444 TD (of the token the is .022, or 2.2%. If)Tj /F6 1 Tf 16.8556 0 TD (W)Tj /F2 1 Tf 0.8889 0 TD ( is a sequence of tokens, then)Tj /F6 1 Tf 13.3733 0 TD (W)Tj /F2 1 Tf 0.8889 0 TD (3 is the third)Tj -32.0067 -1.4444 TD (token, and)Tj /F6 1 Tf 5.0567 0 TD (W)Tj /F2 1 Tf 0.8889 0 TD (1:3 is the sequence of the first through third tokens.)Tj /F6 1 Tf 23.4122 0 TD (P)Tj /F2 1 Tf 0.5567 0 TD (\()Tj /F6 1 Tf 0.3889 0 TD (W)Tj /F2 1 Tf 0.8889 0 TD (i =)Tj /F6 1 Tf 1.1556 0 TD (the)Tj /F2 1 Tf 1.2233 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (W)Tj /F2 1 Tf 0.8889 0 TD (i1=)Tj /F6 1 Tf 1.9344 0 TD (of)Tj /F2 1 Tf 0.8878 0 TD (\) is)Tj -38.06 -1.4444 TD (the)Tj /F6 1 Tf 1.7222 0 TD (conditional probability)Tj /F2 1 Tf 9.0844 0 TD ( of the, given that of is the previous token.)Tj -10.8067 -2.2222 TD (Some details of the Google Corpus: words appearing fewer than 200 times are considered)Tj 0 -1.4444 TD [(unknown)-255.6(and)-256.3(appear)-256.8(as)-255.4(the)-256(symbol)]TJ /F8 1 Tf 8.1 0 0 8.1 270.84 197.75 Tm (\(\)*+,)Tj /F2 1 Tf 9 0 0 9 291.09 197.75 Tm (.)Tj /F6 1 Tf 0.5344 0 TD (N)Tj /F2 1 Tf 0.7222 0 TD [(-grams)-256.1(that)-256.3(occur)-256(fewer)-255.4(than)-257.2(40)-255.8(times)-255.3(are)-256.5(dis-)]TJ -19.6 -1.4444 TD (carded. This policy lessens the effect of typos and helps keep the data set to a mere 24)Tj T* (gigabytes \(compressed\). 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741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 38.01 54.245 c h 37.995 53.76 m 35.511 53.76 33.495 51.744 33.495 49.26 c 33.495 46.776 35.511 44.76 37.995 44.76 c 40.479 44.76 42.495 46.776 42.495 49.26 c 42.495 51.744 40.479 53.76 37.995 53.76 c h 37.995 53.245 m 35.787 53.245 33.995 51.453 33.995 49.245 c 33.995 47.037 35.787 45.245 37.995 45.245 c 40.203 45.245 41.995 47.037 41.995 49.245 c 41.995 51.453 40.203 53.245 37.995 53.245 c h 38.01 52.745 m 36.078 52.745 34.51 51.177 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It consists of five characters, but there are no spaces between them, so a Chinese)Tj T* (reader must perform the task of)Tj /F6 1 Tf 14.4089 0 TD (word segmentation)Tj /F2 1 Tf 7.5289 0 TD (: deciding where the word boundaries)Tj -21.9378 -1.4444 TD [(are.)-251.9(Readers)-253.4(of)-252.3(English)-252(dont)-252.6(normally)-251.9(perform)-252.5(this)-252.3(task,)-252.9(because)-252.3(we)-252.8(have)-252(spaces)-252(between)]TJ T* (words. However, some texts, such as URLs, dont have spaces, and sometimes writers)Tj T* (make mistakes and leave a space out; how could a search engine or word processing pro-)Tj T* (gram correct such a mistake?)Tj 0 -2.2222 TD (Consider the English text choosespain.com. This is a website hoping to convince you to)Tj 0 -1.4444 TD [(choose)-274(Spain)-274.5(as)-275.4(a)-274.4(travel)-274.1(destination,)-273.6(but)-275.7(if)-273.7(you)-274.9(segment)-274.5(the)-273.8(name)-275.4(wrong,)-274.3(you)-273.8(get)-274.8(the)-274.9(less)]TJ T* (appealing name chooses pain. Human readers are able to make the right choice by)Tj T* (drawing upon years of experience; surely it would be an insurmountable task to encode)Tj T* (that experience into a computer algorithm. Yet we can take a shortcut that works surpris-)Tj T* (ingly well: look up each phrase in the bigram table. We see that choose Spain has a)Tj T* [(count)-252.8(of)-252.3(3,210,)-252.2(whereas)-252.6(chooses)-252.1(pain)-253.2(does)-252.3(not)-252.2(appear)-253.4(in)-252.1(the)-252.7(table)-252(at)-252.5(all)-252.9(\(which)-252(means)-253.1(it)]TJ T* [(occurs)-263.6(fewer)-263.2(than)-263.9(40)-263.6(times)-264.2(in)-263.2(the)-263.8(trillion-word)-262.8(corpus\).)-264.6(Thus)-263(choose)-263.3(Spain)-263.9(is)-264.1(at)-263.7(least)-263.3(80)]TJ T* (times more likely, and can be safely considered the right segmentation.)Tj 0 -2.2222 TD (Suppose we were faced with the task of interpreting the phrase insufficientnumbers. If)Tj 0 -1.4444 TD (we add together capitalized and lowercase versions of the words, the counts are:)Tj /F8 1 Tf 8 0 0 8 138 401.42 Tm ( \012% ")Tj 0 -1.25 TD ( \012% )Tj /F2 1 Tf 9 0 0 9 126 373.75 Tm (In sufficient numbers is 50% more frequent than insufficient numbers but thats)Tj 0 -1.4444 TD (hardly compelling evidence. We are left in a frustrating position: we can guess, but we)Tj T* [(cant)-254(be)-253(confident.)-253.5(In)-253.7(uncertain)-253(problems)-253.6(like)-253.5(this,)-253.2(we)-253.9(dont)-253.8(have)-253.1(any)-253.1(way)-253.5(of)-253.4(calculating)-254.1(a)]TJ T* (definitive correct answer, we dont have a complete model of what makes one answer)Tj T* [(right,)-252.1(and)-251.9(in)-253.2(fact)-251.3(human)-252.3(experts)-252.5(dont)-252.6(have)-252(a)-252.2(complete)-251.6(model,)-252.9(either,)-252.1(and)-251.9(can)-252.8(disagree)-252.4(on)]TJ T* (the answer. Still, there is an established methodology for solving uncertain problems:)Tj 0.5111 -2.2222 TD (1.)Tj /F10 1 Tf 1.4889 0 TD (Define a probabilistic model.)Tj /F2 1 Tf 14.3656 0 TD ( We cant define all the factors \(semantic, syntactic,)Tj -14.3656 -1.4444 TD (lexical, and social\) that make choose Spain a better candidate for a domain name,)Tj T* (but we can define a simplified model that gives approximate probabilities. For short)Tj T* (candidates like choose Spain we could just look up the)Tj /F6 1 Tf 25.4322 0 TD (n)Tj /F2 1 Tf 0.5556 0 TD (-gram in the corpus data)Tj -25.9878 -1.4444 TD (and use that as the probability. For longer candidates we will need some way of)Tj T* (composing an answer from smaller parts. For words we havent seen before, well)Tj T* (have to estimate the probability of an unknown word. The point is that we define a)Tj /F6 1 Tf T* (language model)Tj /F2 1 Tf 6.3056 0 TD (a probability distribution over all the strings in the languageand)Tj -6.3056 -1.4444 TD [(learn)-249.8(the)-250.4(parameters)-249.3(of)-250.1(the)-250.4(model)-249.8(from)-249.8(our)-249.5(corpus)-250.5(data,)-249.6(then)-249.4(use)-250(the)-250.4(model)-249.8(to)-249.9(define)]TJ T* (the probability of each candidate.)Tj -1.4889 -1.8889 TD (2.)Tj /F10 1 Tf 1.4889 0 TD [(Enumerate)-262.1(candidates.)]TJ /F2 1 Tf 11.7122 0 TD [(We)-262.2(may)-262.8(not)-262.2(be)-263(sure)-262.1(whether)-262.1(insufficient)-261.8(numbers)-263.2(or)-261.7(in)]TJ -11.7122 -1.4444 TD (sufficient numbers is more likely to be the intended phrase, but we can agree that)Tj T* [(they)-274.5(are)-274.3(both)-274.1(candidate)-274.2(segmentations,)-273.9(as)-274.3(is)-274.1(in)-274.8(suffi)-274.2(cient)-274(numb)-274.1(ers,)-274.4(but)-274.5(that)-274.1(hello)]TJ ET 0 0 0 1 k 239.764 661.781 m 239.741 661.733 239.676 661.708 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53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 38.01 54.245 c h 37.995 53.76 m 35.511 53.76 33.495 51.744 33.495 49.26 c 33.495 46.776 35.511 44.76 37.995 44.76 c 40.479 44.76 42.495 46.776 42.495 49.26 c 42.495 51.744 40.479 53.76 37.995 53.76 c h 37.995 53.245 m 35.787 53.245 33.995 51.453 33.995 49.245 c 33.995 47.037 35.787 45.245 37.995 45.245 c 40.203 45.245 41.995 47.037 41.995 49.245 c 41.995 51.453 40.203 53.245 37.995 53.245 c h 38.01 52.745 m 36.078 52.745 34.51 51.177 34.51 49.245 c 34.51 47.313 36.078 45.745 38.01 45.745 c 39.942 45.745 41.51 47.313 41.51 49.245 c 41.51 51.177 39.942 52.745 38.01 52.745 c h 37.995 52.26 m 36.339 52.26 34.995 50.916 34.995 49.26 c 34.995 47.604 36.339 46.26 37.995 46.26 c 39.651 46.26 40.995 47.604 40.995 49.26 c 40.995 50.916 39.651 52.26 37.995 52.26 c h 37.995 51.745 m 36.615 51.745 35.495 50.625 35.495 49.245 c 35.495 47.865 36.615 46.745 37.995 46.745 c 39.375 46.745 40.495 47.865 40.495 49.245 c 40.495 50.625 39.375 51.745 37.995 51.745 c h 38.01 51.245 m 36.906 51.245 36.01 50.349 36.01 49.245 c 36.01 48.141 36.906 47.245 38.01 47.245 c 39.114 47.245 40.01 48.141 40.01 49.245 c 40.01 50.349 39.114 51.245 38.01 51.245 c h 37.995 50.76 m 37.167 50.76 36.495 50.088 36.495 49.26 c 36.495 48.432 37.167 47.76 37.995 47.76 c 38.823 47.76 39.495 48.432 39.495 49.26 c 39.495 50.088 38.823 50.76 37.995 50.76 c h 37.995 50.245 m 37.443 50.245 36.995 49.797 36.995 49.245 c 36.995 48.693 37.443 48.245 37.995 48.245 c 38.547 48.245 38.995 48.693 38.995 49.245 c 38.995 49.797 38.547 50.245 37.995 50.245 c h 38.01 49.745 m 37.734 49.745 37.51 49.521 37.51 49.245 c 37.51 48.969 37.734 48.745 38.01 48.745 c 38.286 48.745 38.51 48.969 38.51 49.245 c 38.51 49.521 38.286 49.745 38.01 49.745 c s 574 49.25 m 574 57.26 l 569.578 57.26 565.99 53.672 565.99 49.25 c 565.99 44.828 569.578 41.24 574 41.24 c 578.422 41.24 582.01 44.828 582.01 49.25 c 582.01 53.672 578.422 57.26 574 57.26 c f 573.99 57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 20 0 obj > /ExtGState > >> endobj 23 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (222)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 144 678.75 Tm 0 Tc [(world)-234.2(is)-235.2(not)-234.4(a)-234.4(valid)-234.3(candidate.)-235.1(In)-233.7(this)-234.5(step)-234.2(we)-235(withhold)-234.2(judgment)-235.2(and)-234.1(just)-234.5(enumerate)]TJ 0 -1.4444 TD (possibilitiesall the possibilities if we can, or else a carefully selected sample.)Tj -1.4889 -1.8889 TD (3.)Tj /F10 1 Tf 1.4889 0 TD (Choose the most probable candidate.)Tj /F2 1 Tf 18.4278 0 TD ( Apply the language model to each)Tj -18.4278 -1.4444 TD (candidate to get its probability, and choose the one with the highest probability.)Tj -2 -2.2222 TD (If you prefer mathematical equations, the methodology is:)Tj /F6 1 Tf 1.3889 -2.2222 TD (best)Tj /F2 1 Tf 1.5011 0 TD ( = argmax)Tj /F6 1 Tf 7.2 0 0 7.2 192.41 594.32 Tm (c)Tj /F11 1 Tf 0.6111 0 TD ()Tj /F6 1 Tf 0.9917 0 TD (candidates)Tj /F2 1 Tf 9 0 0 9 233.97 595.75 Tm ( P\()Tj /F6 1 Tf 1.2222 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\))Tj -13.5533 -2.4256 TD (Or, if you prefer computer code \(well use Python\), it would be:)Tj /F8 1 Tf 8 0 0 8 138 554.59 Tm (% / \012012 !/ 3)Tj /F2 1 Tf 9 0 0 9 126 536.92 Tm 0.0056 Tc (Lets apply the methodology to segmentation. We want to define a function,)Tj /F8 1 Tf 8.1 0 0 8.1 437.57 536.92 Tm 0.0049 Tc (\012)Tj /F2 1 Tf 9 0 0 9 466.21 536.92 Tm 0 Tc (,)Tj -37.8011 -1.4444 TD 0.0056 Tc (which takes as input a string with no spaces and returns a list of words that is the best)Tj T* (segmentation:)Tj /F8 1 Tf 8 0 0 8 138 491.59 Tm 0 Tc (,,, \01214$43)Tj 0 -1.25 TD (5442 4$46)Tj /F2 1 Tf 9 0 0 9 126 463.92 Tm (Lets start with step 1, the probabilistic language model. The probability of a sequence of)Tj 0 -1.4444 TD (words is the product of the probabilities of each word, given the words context: all the)Tj T* (preceding words. For those who like equations:)Tj 1.3333 -2.2222 TD (P\()Tj /F6 1 Tf 0.9456 0 TD (W)Tj /F2 1 Tf 7.2 0 0 7.2 154.51 416.49 Tm (1:)Tj /F6 1 Tf 0.8333 0 TD (n)Tj /F2 1 Tf 9 0 0 9 164.51 417.92 Tm (\) =)Tj /F11 1 Tf 1.5456 0 TD ()Tj /F6 1 Tf 7.2 0 0 7.2 185.33 416.49 Tm (k)Tj /F2 1 Tf 0.5 0 TD (=1:)Tj /F6 1 Tf 1.4347 0 TD (n)Tj /F2 1 Tf 9 0 0 9 203.26 417.92 Tm (P\()Tj /F6 1 Tf 0.9444 0 TD (W)Tj 7.2 0 0 7.2 219.76 416.49 Tm (k)Tj /F2 1 Tf 9 0 0 9 223.37 417.92 Tm ( |)Tj /F6 1 Tf 0.7778 0 TD (W)Tj /F2 1 Tf 7.2 0 0 7.2 238.37 416.49 Tm (1:)Tj /F6 1 Tf 0.8333 0 TD (k)Tj /F2 1 Tf 0.5 0 TD (1)Tj 9 0 0 9 255.57 417.92 Tm (\))Tj -14.3967 -2.2222 TD (We dont have the data to compute this exactly, so we can approximate the equation by)Tj 0 -1.4444 TD (using a smaller context. Since we have data for sequences up to 5-grams, it would be)Tj T* (tempting to use the 5-grams, so that the probability of an)Tj /F6 1 Tf 25.7056 0 TD (n)Tj /F2 1 Tf 0.5567 0 TD (-word sequence would be the)Tj -26.2622 -1.4444 TD (product of each word given the four previous words \(not all previous words\).)Tj 0 -2.2222 TD (There are three difficulties with the 5-gram model. First, the 5-gram data is about 30)Tj 0 -1.4444 TD [(gigabytes,)-263.5(so)-262.8(it)-263.4(cant)-262.9(all)-262.9(fit)-264(in)-263.2(RAM.)-263.4(Second,)-262.3(many)-264(5-gram)-262.4(counts)-263.7(will)-263.2(be)-263(0,)-263.8(and)-263(wed)-263.2(need)]TJ T* [(some)-272.5(strategy)-272.3(for)]TJ /F6 1 Tf 7.8922 0 TD [(backing)-244.6(off)]TJ /F2 1 Tf 4.3567 0 TD [(,)-273.1(using)-272.1(shorter)-273(sequences)-272.2(to)-273.2(estimate)-272.3(the)-272.7(5-gram)-272.4(probabilities.)]TJ -12.2489 -1.4444 TD [(Third,)-254.2(the)-253.8(search)-253.6(space)-254.3(of)-253.4(candidates)-254.1(will)-254.3(be)-254.1(large)-254.1(because)-253.4(dependencies)-254.5(extend)-254(up)-254.1(to)-254.3(four)]TJ T* (words away. All three of these difficulties can be managed, with some effort. But instead,)Tj T* [(lets)-272(first)-271.5(consider)-271.4(a)-271.1(much)-271.5(simpler)-272(language)-271.1(model)-272(that)-270.8(solves)-272.1(all)-270.7(three)-271.4(difficulties)-271.6(at)-271.4(once:)]TJ T* (a unigram model, in which the probability of a sequence is just the product of the proba-)Tj T* (bility of each word by itself. In this model, the probability of each word is independent of)Tj T* (the other words:)Tj 1.1111 -2.2222 TD (P\()Tj /F6 1 Tf 0.9444 0 TD (W)Tj /F2 1 Tf 7.2 0 0 7.2 152.5 213.49 Tm (1:)Tj /F6 1 Tf 0.8347 0 TD (n)Tj /F2 1 Tf 9 0 0 9 162.51 214.92 Tm (\) =)Tj /F11 1 Tf 1.5444 0 TD ()Tj /F6 1 Tf 7.2 0 0 7.2 183.33 213.49 Tm (k)Tj /F2 1 Tf 0.5 0 TD (=1:)Tj /F6 1 Tf 1.4333 0 TD (n)Tj /F2 1 Tf 9 0 0 9 201.26 214.92 Tm (P\()Tj /F6 1 Tf 0.9444 0 TD (W)Tj 7.2 0 0 7.2 217.76 213.49 Tm (k)Tj /F2 1 Tf 9 0 0 9 221.36 214.92 Tm (\))Tj -10.5956 -2.4256 TD (To segment)Tj /F8 1 Tf 8.1 0 0 8.1 174.5 193.09 Tm (47\0124)Tj /F2 1 Tf 9 0 0 9 223.1 193.09 Tm (, we consider candidates such as)Tj /F8 1 Tf 8.1 0 0 8.1 354.46 193.09 Tm (7 \012)Tj /F2 1 Tf 9 0 0 9 403.05 193.09 Tm (, and compute)Tj -30.7833 -1.4444 TD (P\()Tj /F6 1 Tf 0.9456 0 TD (when)Tj /F2 1 Tf 2.2222 0 TD (\))Tj /F11 1 Tf 0.5556 0 TD ()Tj /F2 1 Tf 0.7144 0 TD (P\()Tj /F6 1 Tf 0.9456 0 TD (in)Tj /F2 1 Tf 0.8333 0 TD (\))Tj /F11 1 Tf 0.5556 0 TD ()Tj /F2 1 Tf 0.7144 0 TD (P\()Tj /F6 1 Tf 0.9456 0 TD (rome)Tj /F2 1 Tf 2 0 TD [(\).)-249.7(If)-249.7(the)-249.3(product)-249.4(is)-249.7(higher)-248.8(than)-249.4(any)-249.8(other)-249.9(candidates)-249.4(product,)-249.2(then)]TJ -10.4322 -1.4444 TD (thats the best answer.)Tj 0 -2.2222 TD (An)Tj /F6 1 Tf 1.6111 0 TD (n)Tj /F2 1 Tf 0.5556 0 TD (-character string has 2)Tj /F6 1 Tf 6 0 0 6 234.5 150.12 Tm (n)Tj /F2 1 Tf 0.5567 0 TD (1)Tj 9 0 0 9 244.18 147.09 Tm ( different segmentations \(there are)Tj /F6 1 Tf 15.6856 0 TD (n)Tj /F2 1 Tf 0.5555 0 TD (1 positions between)Tj -29.3722 -1.4444 TD (characters, each of which can either be or not be a word boundary\). Thus the string)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 222 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 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49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 24 0 obj > /ExtGState > >> endobj 27 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (223)Tj /F8 1 Tf 8.1 0 0 8.1 126 678.75 Tm (47\0128%\0124)Tj /F2 1 Tf 9 0 0 9 320.4 678.75 Tm ( has 35 trillion segmentations. But Im)Tj -21.6 -1.4444 TD (sure you were able to find the right segmentation in just a few seconds; clearly, you)Tj T* [(couldnt)-231.9(have)-232(enumerated)-233.1(all)-231.8(the)-232.7(candidates.)-231.6(You)-232(probably)-232.2(scanned)-232.3(w,)-232.3(wh,)-232.4(and)-231.9(whe)]TJ T* (and rejected them as improbable words, but accepted when as probable. Then you)Tj T* (moved on to the remainder and found its best segmentation. Once we make the simplify-)Tj T* (ing assumption that each word is independent of the others, it means that we dont have)Tj T* (to consider all combinations of words.)Tj 0 -2.2222 TD [(That)-267.8(gives)-267.1(us)-267.8(a)-267.8(sketch)-268.1(of)-267.9(the)]TJ /F8 1 Tf 8.1 0 0 8.1 240.53 580.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 271.29 580.75 Tm [(function:)-268.5(consider)-267(every)-268.1(possible)-267(way)-268(to)-267.7(split)-268.2(the)-267.1(text)]TJ -16.1433 -1.4444 TD (into a first word and a remaining text \(we can arbitrarily limit the longest possible word)Tj T* (to, say,)Tj /F6 1 Tf 3.4267 0 TD (L)Tj /F2 1 Tf 0.5567 0 TD (=20 letters\). For each possible split, find the best way to segment the remainder.)Tj -3.9833 -1.4444 TD -0.0156 Tc [(Out)-244.8(of)-243.5(all)-245.1(the)-244.9(possible)-247(candidates,)-248.3(the)-244.9(one)-244.1(w)-0.1(ith)-245.2(the)-244.9(h)0(ighest)-246.9(p)0(roduct)-246.1(of)-244.6(P\()]TJ /F6 1 Tf 30.8189 0 TD (first)Tj /F2 1 Tf 1.4822 0 TD 0 Tc (\))Tj /F11 1 Tf 0.51 0 TD ()Tj /F2 1 Tf 0.7 0 TD -0.0155 Tc (P\()Tj /F6 1 Tf 0.9156 0 TD (remaining)Tj /F2 1 Tf 4.0322 0 TD 0.2288 Tc [(\)i)228.8(s)]TJ -38.4589 -1.4444 TD 0 Tc (the best.)Tj 0 -2.2222 TD (Here we show a table of choices for the first word, probability of the word, probability of)Tj 0 -1.4444 TD [(the)-277.1(best)-277.7(segmentation)-278.7(of)-276.8(the)-278.2(remaining)-277.2(words,)-278.1(and)-277.4(probability)-277.6(of)-277.9(the)-277.1(whole)-277.8(\(which)-277.5(is)-278.6(the)]TJ T* (product of the probabilities of the first and the remainder\). We see that the segmentation)Tj T* (starting with when is 50,000 times better than the second-best candidate.)Tj 0 -14.0556 TD (We can implement)Tj /F8 1 Tf 8.1 0 0 8.1 204.49 343.25 Tm (\012)Tj /F2 1 Tf 9 0 0 9 232.84 343.25 Tm ( in a few lines of Python:)Tj /F8 1 Tf 8 0 0 8 138 323.92 Tm (9\012\012)Tj 0 -1.25 TD ()Tj /F13 1 Tf 2 0 TD ()Tj /F8 1 Tf 3.5 0 TD (103:)Tj -5.5 -1.25 TD ( ;# 7 % \012 0 0: 56)Tj T* ( / 156=\0121\0123 2\012 $1033)Tj T* ( \012012 !/ 73)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 3 0 TD (102 >/3:)Tj -5 -1.25 TD ( ;# $% 12 \0123 $2 13\(/> 5105:="62 05=":63)Tj T* ( 1\01211032 >336)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD (\012\015)Tj /F8 1 Tf 3 0 TD (173:)Tj -5 -1.25 TD ( ;& *8 ? $%% 7 $1 7173 7 73)Tj /F6 1 Tf 9 0 0 9 126 166.25 Tm (This is the entire program)Tj /F2 1 Tf 10.2822 0 TD (with three minor omissions:)Tj /F8 1 Tf 8.1 0 0 8.1 342.88 166.25 Tm ($)Tj /F2 1 Tf 9 0 0 9 371.23 166.25 Tm ( is a utility function that)Tj -27.2478 -1.4444 TD [(multiplies)-259.8(together)-260.2(a)-260(list)-260.9(of)-260.1(numbers,)]TJ /F8 1 Tf 8.1 0 0 8.1 274.71 153.25 Tm (\012\012)Tj /F2 1 Tf 9 0 0 9 293.26 153.25 Tm [(is)-259.7(a)-260(decorator)-260.3(that)-259.7(caches)-259.8(the)-260.4(results)-259.9(of)-260.1(previous)]TJ -18.5844 -1.4444 TD [(calls)-256.5(to)-256.6(a)-255.6(function)-256.5(so)-256.1(that)-256.3(they)-255.7(dont)-257.1(have)-255.3(to)-256.6(be)-256.3(recomputed,)-256.7(and)]TJ /F8 1 Tf 8.1 0 0 8.1 384.82 140.25 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 395.22 140.25 Tm [(estimates)-256.6(the)-256(probabil-)]TJ -29.9133 -1.4444 TD (ity of a word by consulting the unigram count data.)Tj /F15 1 Tf 8 0 0 8 132 445.22 Tm (first)Tj /F1 1 Tf 11.25 0 TD (P\()Tj /F15 1 Tf 0.8025 0 TD (first)Tj /F1 1 Tf 1.625 0 TD 8.5275 Tc [(\)P)8527.5(\()]TJ /F15 1 Tf 9.625 0 TD 0 Tc (remaining)Tj /F1 1 Tf 4.0162 0 TD 6.1362 Tc [(\)P)6136.2(\()]TJ /F15 1 Tf 7.2338 0 TD 0 Tc (first)Tj /F1 1 Tf 1.625 0 TD (\))Tj /F11 1 Tf 0.64 0 TD ()Tj /F1 1 Tf 0.715 0 TD ( P\()Tj /F15 1 Tf 0.9825 0 TD (remaining)Tj /F1 1 Tf 4.0163 0 TD (\))Tj /F3 1 Tf -42.5312 -1.625 TD [(w)-10595(210)]TJ 6 0 0 6 235.57 433.82 Tm (4)Tj 8 0 0 8 312 432.22 Tm (210)Tj 6 0 0 6 325.57 433.82 Tm (33)Tj 8 0 0 8 402 432.22 Tm (610)Tj 6 0 0 6 415.57 433.82 Tm (37)Tj 8 0 0 8 132 419.22 Tm [(wh)-10101(510)]TJ 6 0 0 6 235.64 420.82 Tm (6)Tj 8 0 0 8 312 419.22 Tm (610)Tj 6 0 0 6 325.57 420.82 Tm (33)Tj 8 0 0 8 402 419.22 Tm (310)Tj 6 0 0 6 415.57 420.82 Tm (38)Tj 8 0 0 8 132 406.22 Tm [(whe)-9645(310)]TJ 6 0 0 6 235.57 407.82 Tm (7)Tj 8 0 0 8 312 406.22 Tm (310)Tj 6 0 0 6 325.57 407.82 Tm (32)Tj 8 0 0 8 402 406.22 Tm (710)Tj 6 0 0 6 415.57 407.82 Tm (39)Tj 8 0 0 8 132 393.22 Tm [(when)-9151(610)]TJ 6 0 0 6 235.57 394.82 Tm (4)Tj 8 0 0 8 312 393.22 Tm (710)Tj 6 0 0 6 325.57 394.82 Tm (29)Tj 8 0 0 8 402 393.22 Tm (410)Tj 6 0 0 6 415.57 394.82 Tm (32)Tj 8 0 0 8 132 380.22 Tm [(wheni)-8897(110)]TJ 6 0 0 6 235.57 381.82 Tm (16)Tj 8 0 0 8 312 380.22 Tm (310)Tj 6 0 0 6 325.57 381.82 Tm 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0 0 8.1 162 678.75 Tm (\012\012)Tj /F2 1 Tf 9 0 0 9 178.2 678.75 Tm (, a call to)Tj /F8 1 Tf 8.1 0 0 8.1 216.71 678.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 245.06 678.75 Tm ( for an)Tj /F6 1 Tf 3.2056 0 TD (n)Tj /F2 1 Tf 0.5556 0 TD (-character text makes 2)Tj /F6 1 Tf 6 0 0 6 372.91 681.78 Tm (n)Tj /F2 1 Tf 9 0 0 9 376.24 678.75 Tm ( recursive calls to)Tj /F8 1 Tf 8.1 0 0 8.1 447.58 678.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 475.93 678.75 Tm (;)Tj -38.8811 -1.4444 TD (with)Tj /F8 1 Tf 8.1 0 0 8.1 146.84 665.75 Tm (\012\012)Tj /F2 1 Tf 9 0 0 9 163.04 665.75 Tm ( it makes only)Tj /F6 1 Tf 6.5378 0 TD (n)Tj /F2 1 Tf 0.5556 0 TD ( calls)Tj /F8 1 Tf 8.1 0 0 8.1 255.38 665.75 Tm (\012\012)Tj /F2 1 Tf 9 0 0 9 271.58 665.75 Tm ( makes this a fairly efficient dynamic programming)Tj -16.1756 -1.4444 TD [(algorithm.)-255.6(Each)-255.1(of)-255.7(the)]TJ /F6 1 Tf 10.1133 0 TD (n)Tj /F2 1 Tf 0.8111 0 TD [(calls)-255.4(considers)-255.7(O\()]TJ /F6 1 Tf 7.66 0 TD (L)Tj /F2 1 Tf 0.5567 0 TD [(\))-255.4(splits,)-254.5(and)-256.3(evaluates)-255.3(each)-255(split)-254.9(by)-256(multiplying)]TJ -19.1411 -1.4444 TD (O\()Tj /F6 1 Tf 1.1478 0 TD (n)Tj /F2 1 Tf 0.5567 0 TD (\) probabilities, so the whole algorithm is O\()Tj /F6 1 Tf 19.3189 0 TD (n)Tj /F2 1 Tf 6 0 0 6 320.21 642.78 Tm (2)Tj /F6 1 Tf 9 0 0 9 323.55 639.75 Tm (L)Tj /F2 1 Tf 0.5556 0 TD (\).)Tj -22.5056 -2.2222 TD (As for)Tj /F8 1 Tf 8.1 0 0 8.1 152.34 619.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 160.44 619.75 Tm (, we read in the unigram counts from a datafile. If a word appears in the corpus,)Tj -3.8267 -1.4445 TD [(its)-270(estimated)-269.6(probability)-269.8(is)-269.7(Count\()]TJ /F6 1 Tf 14.9689 0 TD (word)Tj /F2 1 Tf 2.0544 0 TD [(\)/N,)-269.8(where)]TJ /F6 1 Tf 5.1333 0 TD (N)Tj /F2 1 Tf 0.9911 0 TD [(is)-269.7(the)-270.4(corpus)-269.4(size.)-269.9(Actually,)-269(instead)-269.6(of)]TJ -23.1478 -1.4444 TD (using the full 13-million-type unigram datafile, I created)Tj /F8 1 Tf 8.1 0 0 8.1 354.52 593.75 Tm (8%@\012\012)Tj /F2 1 Tf 9 0 0 9 403.12 593.75 Tm (, which \(a\) is case-)Tj -30.7911 -1.4444 TD [(insensitive,)-276.8(so)-276.1(that)-276.3(the)-277.1(counts)-276(for)-276.7(the,)-276.6(The,)-277(and)-276.3(THE)-276.3(are)-276.5(added)-276.4(together)-276.9(under)-276.3(a)-276.7(sin-)]TJ T* (gle entry for the; \(b\) only has entries for words made out of letters, not numbers or)Tj T* (punctuation \(so +170.002 is out, as is cant\); and \(c\) lists only the most common 1/3)Tj T* (of a million words \(which together cover 98% of the tokens\).)Tj 0 -2.2222 TD (The only tricky part of)Tj /F8 1 Tf 8.1 0 0 8.1 218.02 521.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 226.12 521.75 Tm ( is when a word has not been seen in the corpus. This happens)Tj -11.1244 -1.4444 TD (sometimes even with a trillion-word corpus, so it would be a mistake to return 0 for the)Tj T* (probability. But what should it be? The number of tokens in the corpus,)Tj /F6 1 Tf 32.2656 0 TD (N)Tj /F2 1 Tf 0.7211 0 TD (, is about a tril-)Tj -32.9867 -1.4444 TD (lion, and the least common word in)Tj /F8 1 Tf 8.1 0 0 8.1 271.85 482.75 Tm (8%@\012\012)Tj /F2 1 Tf 9 0 0 9 320.45 482.75 Tm ( has a count of 12,711. So a previously)Tj -21.6056 -1.4444 TD (unseen word should have a probability of somewhere between 0 and 12,710/)Tj /F6 1 Tf 34.5089 0 TD (N)Tj /F2 1 Tf 0.7222 0 TD (. Not all)Tj -35.2311 -1.4444 TD (unseen words are equally unlikely: a random sequence of 20 letters is less likely to be a)Tj T* (word than a random sequence of 6 letters. We will define a class for probability distribu-)Tj T* (tions,)Tj /F8 1 Tf 8.1 0 0 8.1 150.51 430.75 Tm ( )Tj /F2 1 Tf 9 0 0 9 170.76 430.75 Tm (, which loads a datafile of \(key, count\) pairs. By default, the probability of an)Tj -4.9733 -1.4444 TD (unknown word is 1/)Tj /F6 1 Tf 9.1333 0 TD (N)Tj /F2 1 Tf 0.7222 0 TD (, but each instance of a)Tj /F8 1 Tf 8.1 0 0 8.1 309.37 417.75 Tm ( )Tj /F2 1 Tf 9 0 0 9 329.62 417.75 Tm ( can supply a custom function to over-)Tj -22.6244 -1.4444 TD (ride the default. We want to avoid having too high a probability for very long words, so)Tj T* (we \(rather arbitrarily\) start at a probability of 10/)Tj /F6 1 Tf 21.8756 0 TD (N)Tj /F2 1 Tf 0.7211 0 TD (, and decrease by a factor of 10 for)Tj -22.5967 -1.4444 TD (every letter in the candidate word. We then define)Tj /F8 1 Tf 8.1 0 0 8.1 331.36 378.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 339.46 378.75 Tm ( as a)Tj /F8 1 Tf 8.1 0 0 8.1 359.47 378.75 Tm ( )Tj /F2 1 Tf 9 0 0 9 379.72 378.75 Tm (:)Tj /F8 1 Tf 8 0 0 8 138 359.42 Tm ()Tj /F13 1 Tf 3 0 TD (\012 )Tj /F8 1 Tf 2.5 0 TD (13:)Tj -5.5 -1.25 TD ( ;\015 $%% % \012 \012 @)-166.3(@@)-166.3(@12 2 */*2 \012/*3:)]TJ T* ( !2 :)Tj T* ( 5!6 / 1!2 3 = 13)Tj T* [( 1* \012181)-166.6(333)]TJ T* ( / \012 1\012% !2 *: "<. t> @)-166.3(@@)-166.3(@12 !3:)]TJ T* ( ! : 5!6.: 1!2 )Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 4 0 TD (1\0122 $/4A43:)Tj -6 -1.25 TD ( ;# !28 $ \012 1\0123:)Tj T* ( $1$3)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD ( \015)Tj /F8 1 Tf 8 0 TD (172 *3:)Tj -10 -1.25 TD ( ;B\012 $%% !7 7 "<.1 c>CC1733)Tj /F13 1 Tf 0 -2.5 TD ()Tj /F8 1 Tf 0.5 0 TD ( / "'' DD *\012% ! $)Tj /F13 1 Tf -0.5 -2.5 TD (\012)Tj /F8 1 Tf 1 0 TD ( / 1148%@\012\012432 *2 8@@733)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 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57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 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567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 33 0 obj > /ExtGState > >> endobj 35 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (225)Tj /F2 1 Tf 9 0 0 9 126 678.75 Tm [(Note)-244.5(that)]TJ /F8 1 Tf 8.1 0 0 8.1 165.39 678.75 Tm ( 7576)Tj /F2 1 Tf 9 0 0 9 187.84 678.75 Tm [(is)-244.1(the)-244.9(raw)-243.8(count)-245(for)-244.4(word)]TJ /F8 1 Tf 8.1 0 0 8.1 290.55 678.75 Tm (7)Tj /F2 1 Tf 9 0 0 9 294.6 678.75 Tm [(,)-244.2(while)]TJ /F8 1 Tf 8.1 0 0 8.1 323.84 678.75 Tm ( 7173)Tj /F2 1 Tf 9 0 0 9 346.29 678.75 Tm [(is)-244.1(the)-244.9(probability.)-244.1(All)-244.2(the)-244.9(programs)]TJ -24.4767 -1.4444 TD (described in this article are available at)Tj /F6 1 Tf 17.4467 0 TD (http://norvig.com/ngrams)Tj /F2 1 Tf 10.2267 0 TD (.)Tj -27.6733 -2.2222 TD (So how well does this model do at segmentation? Here are some examples:)Tj /F8 1 Tf 8 0 0 8 138 626.42 Tm (,,, \01214$43)Tj 0 -1.25 TD (5442 4$46)Tj T* (,,, \0121443)Tj T* (5442 442 442 446)Tj T* (,,, \012147\0128%\01243)Tj T* (54742 442 442 442 442 4\01242 4842 442 4%\01242 446)Tj T* (,,, \012147$43)Tj T* (54742 4$46)Tj T* (,,, \012140$043)Tj T* (540$42 4046)Tj T* (,,, \01214$43)Tj T* (54$42 442 446)Tj T* (,,, \012147\01243)Tj T* (54742 442 442 4\01242 442 442 446)Tj T* (,,, \012148!743)Tj T* (5442 442 442 442 4842 4!746)Tj T* (,,, \012147%$!7!43)Tj T* (5442 4742 442 4%42 442 442 442 4$42 442 442 4!42)Tj T* (4742 4!42 446)Tj T* (,,, \012147%\01277\01277\0127)Tj T* (43)Tj T* [(5442)-458.8(4742)-457.5(442)-458.8(4%42)-458.8(442)-457.5(4\01242)-458.8(442)-458.8(4742)-457.5(442)-458.8(4742)-458.8(442)-457.5(4\01242)]TJ T* (442 4742 442 442 442 47\01242 442 4742 442 442 442)Tj T* (446)Tj T* (,,, \01214\0127!\012\012\012\012\012)Tj T* (%43)Tj T* (5442 442 4\01242 47!42 442 4\01242 4\01242 442 4\01242 442)Tj T* (442 4\01242 4\01242 442 442 4%42 442 442 442)Tj T* (446)Tj T* (,,, \012148%%77)Tj T* (7\012E\012%77)Tj T* (7%%\012\01243)Tj T* [(5442)-458.8(442)-457.5(442)-458.8(442)-458.8(442)-457.5(442)-458.8(442)-458.8(4842)-457.5(442)-458.8(4%%42)-458.8(442)-457.5(442)]TJ T* [(442)-455.1(442)-453.8(4742)-455(442)-455(442)-453.8(4742)-455(442)-453.8(442)-455(442)-455(47\01242)-453.8(442)]TJ T* (442 4E42 4\01242 442 442 442 442 4%42 442 442 4742)Tj T* (442 442 442 442 4742 442 442 442 442 442 4742 442)Tj T* (4%%42 442 442 442 4\01242 4\01246)Tj T* (,,, \01214%!7%7$)Tj T* (\0120\012743)Tj T* (5442 442 442 442 442 4%!742 442 442 4%42)Tj T* (442 442 442 4742 4$42 4\01242 442 442 4042 442 442)Tj T* (4\01242 442 442 4742 446)Tj /F2 1 Tf 9 0 0 9 126 198.75 Tm (The reader might be pleased to see the program correctly segmented such unusual words)Tj 0 -1.4444 TD (as Samsa and oozy. You shouldnt be surprised: Samsa appears 42,000 times and)Tj T* (oozy 13,000 times in the trillion-word corpus. Overall the results look good, but there)Tj T* (are two errors:)Tj /F8 1 Tf 8.1 0 0 8.1 187.35 159.75 Tm (44244)Tj /F2 1 Tf 9 0 0 9 248.1 159.75 Tm ( should be one word, and)Tj /F8 1 Tf 8.1 0 0 8.1 352.81 159.75 Tm (474)Tj /F2 1 Tf 9 0 0 9 389.26 159.75 Tm ( should be two. Still,)Tj -29.2511 -1.4444 TD (thats a word precision rate of 157/159 = 98.7%; not too bad.)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 225 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 38.01 54.245 c h 37.995 53.76 m 35.511 53.76 33.495 51.744 33.495 49.26 c 33.495 46.776 35.511 44.76 37.995 44.76 c 40.479 44.76 42.495 46.776 42.495 49.26 c 42.495 51.744 40.479 53.76 37.995 53.76 c h 37.995 53.245 m 35.787 53.245 33.995 51.453 33.995 49.245 c 33.995 47.037 35.787 45.245 37.995 45.245 c 40.203 45.245 41.995 47.037 41.995 49.245 c 41.995 51.453 40.203 53.245 37.995 53.245 c h 38.01 52.745 m 36.078 52.745 34.51 51.177 34.51 49.245 c 34.51 47.313 36.078 45.745 38.01 45.745 c 39.942 45.745 41.51 47.313 41.51 49.245 c 41.51 51.177 39.942 52.745 38.01 52.745 c h 37.995 52.26 m 36.339 52.26 34.995 50.916 34.995 49.26 c 34.995 47.604 36.339 46.26 37.995 46.26 c 39.651 46.26 40.995 47.604 40.995 49.26 c 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569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 36 0 obj > /ExtGState > >> endobj 38 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (226)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 126 678.75 Tm 0 Tc (The first error is in part because unregarded does not appear in our 1/3-million-word)Tj 0 -1.4444 TD [(vocabulary.)-260.7(\(It)]TJ /F6 1 Tf 6.7411 0 TD (is)Tj /F2 1 Tf 0.8722 0 TD [(in)-259.9(the)-260.4(full)-260.2(13-million-word)-260.3(vocabulary)-259.8(at)-260.3(position)-259.6(1,005,493,)-260.6(with)-259.7(count)]TJ -7.6133 -1.4444 TD (7,557.\) If we put it in the vocabulary, we see that the segmentation is correct:)Tj /F8 1 Tf 8 0 0 8 138 633.42 Tm (,,, 75446 / )Tj 0 -1.25 TD (,,, \01214%!7%7$)Tj T* (\0120\012743)Tj T* (5442 442 442 442 442 4%!742 442 442 4%42)Tj T* (442 442 442 4742 4$42 4\01242 442 442 4042 442 442)Tj T* (4\01242 442 4742 446)Tj /F2 1 Tf 9 0 0 9 126 565.75 Tm (That doesnt prove weve solved the problem: we would have to put back all the other)Tj 0 -1.4444 TD (intervening words, not just the one we wanted, and we would have to then rerun all the)Tj T* (test cases to make sure that adding the other words did not mess up any other result.)Tj 0 -2.2222 TD (The second error happens because, although sit and down are common words \(with)Tj 0 -1.4444 TD (probability .003% and .04%, respectively\), the product of their two probabilities is just)Tj T* (slightly less than the probability of sitdown by itself. However, the probability of the)Tj T* (two-word sequence sit down, according to the bigram counts, is about 100 times)Tj T* (greater. We can try to fix this problem by modeling bigrams; that is, considering the prob-)Tj T* (ability of each word, given the previous word:)Tj 1.1111 -2.2222 TD (P\()Tj /F6 1 Tf 0.9444 0 TD (W)Tj /F2 1 Tf 7.2 0 0 7.2 152.5 433.32 Tm (1:)Tj /F6 1 Tf 0.8347 0 TD (n)Tj /F2 1 Tf 9 0 0 9 162.51 434.75 Tm (\) =)Tj /F11 1 Tf 1.5444 0 TD ()Tj /F6 1 Tf 7.2 0 0 7.2 183.33 433.32 Tm (k)Tj /F2 1 Tf 0.5 0 TD (=1:)Tj /F6 1 Tf 1.4333 0 TD (n)Tj /F2 1 Tf 9 0 0 9 201.26 434.75 Tm (P\()Tj /F6 1 Tf 0.9444 0 TD (W)Tj 7.2 0 0 7.2 217.76 433.32 Tm (k)Tj /F2 1 Tf 9 0 0 9 221.36 434.75 Tm ( |)Tj /F6 1 Tf 0.7778 0 TD (W)Tj 7.2 0 0 7.2 236.36 433.32 Tm (k)Tj /F2 1 Tf 0.5 0 TD (1)Tj 9 0 0 9 247.57 434.75 Tm (\))Tj -13.5078 -2.4256 TD (Of course the complete bigram table wont fit into memory. If we keep only bigrams that)Tj 0 -1.4444 TD [(appear)-276.8(100,000)-278.2(or)-277.2(more)-277(times,)-277.3(that)-277.4(works)-277.2(out)-276.7(to)-277.7(a)-276.7(little)-277.8(over)-276.9(250,000)-277.1(entries,)-277.5(which)-277.6(does)]TJ T* (fit. We can then estimate P\()Tj /F6 1 Tf 12.37 0 TD (down)Tj /F2 1 Tf 2.2222 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (sit)Tj /F2 1 Tf 0.89 0 TD (\) as Count\()Tj /F6 1 Tf 5.0011 0 TD (sit down)Tj /F2 1 Tf 3.3622 0 TD (\)/Count\()Tj /F6 1 Tf 3.9444 0 TD (sit)Tj /F2 1 Tf 0.89 0 TD (\). If a bigram does not)Tj -29.4578 -1.4444 TD (appear in the table, then we just fall back on the unigram value. We can define)Tj /F8 1 Tf 8.1 0 0 8.1 445.54 373.92 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 457.69 373.92 Tm (, the)Tj -36.8544 -1.4444 TD (conditional probability of a word given the previous word, as:)Tj /F8 1 Tf 8 0 0 8 138 341.59 Tm ()Tj /F13 1 Tf 2 0 TD (\012)Tj /F8 1 Tf 1.5 0 TD (172 $83:)Tj -3.5 -1.25 TD ( ;& $%% 17 F $8G73:)Tj T* ( 75$8 = 4 4 = 76.1 75$863)Tj T* ( 0$ +B:)Tj T* ( 7173)Tj 0 -2.5 TD ( 7 / 1147432 *3)Tj /F2 1 Tf 9 0 0 9 126 253.92 Tm [(\(Purists)-263.7(will)-263.2(note)]TJ /F8 1 Tf 8.1 0 0 8.1 195.96 253.92 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 210.48 253.92 Tm [(is)-263(not)-263.3(a)-264.4(probability)-263.2(distribution,)-262.9(because)-263.4(the)-263.8(sum)-263.1(over)-263.5(all)-262.9(words)-263.9(for)-263.3(a)]TJ -9.3867 -1.4444 TD (given previous word can be greater than 1. This approach has the technical name)Tj /F6 1 Tf 36.43 0 TD (stupid)Tj -36.43 -1.4444 TD (backoff)Tj /F2 1 Tf 2.8344 0 TD (, but it works well in practice, so we wont worry about it.\) We can now compare)Tj -2.8344 -1.4444 TD (sitdown to sit down with a preceding to:)Tj /F8 1 Tf 8 0 0 8 138 195.59 Tm (,,, 71442 443C 714742 443 . 714742 443)Tj 0 -1.25 TD ("'"'')Tj /F2 1 Tf 9 0 0 9 126 167.92 Tm (We see that sit down is 1,698 times more likely than sitdown, because sit down is a)Tj 0 -1.4444 TD (popular bigram, and because to sit is popular but to sitdown is not.)Tj 0 -2.2222 TD (This looks promising; lets implement a new version of)Tj /F8 1 Tf 8.1 0 0 8.1 347.05 134.92 Tm (\012)Tj /F2 1 Tf 9 0 0 9 375.4 134.92 Tm ( using a bigram model.)Tj -27.7111 -1.4444 TD (While were at it, well fix two other issues:)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 226 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 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7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (227)Tj /F2 1 Tf 9 0 0 9 130.6 678.75 Tm [(1.)-654.9(When)]TJ /F8 1 Tf 8.1 0 0 8.1 171 678.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 199.35 678.75 Tm ( added one new word to a sequence of)Tj /F6 1 Tf 17.45 0 TD (n)Tj /F2 1 Tf 0.5556 0 TD ( words segmented in the)Tj -24.1556 -1.4444 TD (remainder, it called)Tj /F8 1 Tf 8.1 0 0 8.1 224.01 665.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 248.31 665.75 Tm ( to multiply together all)Tj /F6 1 Tf 10.8156 0 TD (n)Tj /F2 1 Tf 0.5567 0 TD (+1 probabilities. But)Tj /F8 1 Tf 8.1 0 0 8.1 434.25 665.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 462.6 665.75 Tm ( had)Tj -35.4 -1.4444 TD [(already)-266.6(multiplied)-267.3(all)-267.3(the)-267.1(probabilities)-266.5(in)-267.7(the)-267.1(remainder.)-266.5(It)-267.2(would)-267.3(be)-266.3(more)-267(efficient)-268.2(to)]TJ T* [(remember)-254.5(the)-254.9(probability)-255.4(of)-255.7(the)-254.9(remainder)-254.5(and)-255.2(then)-255(just)-254.5(do)-254.7(one)-255.2(more)-254.8(multiplication.)]TJ -1.4889 -1.8889 TD [(2.)-654.9(There is a potential problem with arithmetic underflow. If we apply)]TJ /F8 1 Tf 8.1 0 0 8.1 416.87 622.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 441.17 622.75 Tm ( to a)Tj -33.0189 -1.4444 TD (sequence consisting of the word blah repeated 61 times, we get 5.2)Tj 7 0 0 7 419.88 609.75 Tm ()Tj 9 0 0 9 423.38 609.75 Tm (10)Tj 8.1 0 0 8.1 433.39 612.53 Tm (321)Tj 9 0 0 9 450.95 609.75 Tm (, but if)Tj -34.1056 -1.4444 TD [(we)-257.2(add)-258(one)-258.5(more)-257(blah,)-258(we)-258.3(get)-257(0.0.)-258.6(The)-257.4(smallest)-257.2(positive)-258.5(floating-point)-257(number)-258.4(that)]TJ T* (can be represented is about 4.9)Tj 7 0 0 7 268.19 583.75 Tm ()Tj 9 0 0 9 271.69 583.75 Tm (10)Tj 6.75 0 0 6.75 281.7 587.77 Tm (324)Tj 9 0 0 9 296.33 583.75 Tm (; anything smaller than that rounds to 0.0. To)Tj -16.9256 -1.4444 TD (avoid underflow, the simplest solution is to add logarithms of numbers rather than)Tj T* (multiplying the numbers themselves.)Tj -2 -2 TD (We will define)Tj /F8 1 Tf 8.1 0 0 8.1 186.69 539.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 219.09 539.75 Tm (, which differs from)Tj /F8 1 Tf 8.1 0 0 8.1 300.44 539.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 328.79 539.75 Tm ( in three ways: first, it uses a condi-)Tj -22.5322 -1.4444 TD (tional bigram language model,)Tj /F8 1 Tf 8.1 0 0 8.1 250.34 526.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 262.49 526.75 Tm (, rather than the unigram model)Tj /F8 1 Tf 8.1 0 0 8.1 394.99 526.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 403.09 526.75 Tm (. Second, the func-)Tj -30.7878 -1.4444 TD [(tion)-272(signature)-272.3(is)-271.9(different.)-272.7(Instead)-272.3(of)-272.3(being)-271.8(passed)-272.2(a)-272.2(single)-272.9(argument)-272.4(\(the)-271.4(text\),)]TJ /F8 1 Tf 8.1 0 0 8.1 442.7 513.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 477.55 513.75 Tm (is)Tj -39.0611 -1.4444 TD (also passed the previous word. At the start of the sentence, the previous word is the spe-)Tj T* (cial beginning-of-sentence marker,)Tj /F8 1 Tf 8.1 0 0 8.1 268.17 487.75 Tm (\(-,)Tj /F2 1 Tf 9 0 0 9 280.32 487.75 Tm (. The return value is not just a list of words, but)Tj -17.1467 -1.4444 TD (rather a pair of values: the probability of the segmentation, followed by the list of words.)Tj T* (We return the probability so that it can be stored \(by)Tj /F8 1 Tf 8.1 0 0 8.1 339.52 461.75 Tm (\012\012)Tj /F2 1 Tf 9 0 0 9 355.73 461.75 Tm (\) and need not be recomputed;)Tj -25.5256 -1.4444 TD (this fixes problem \(1\), the inefficiency. The function)Tj /F8 1 Tf 8.1 0 0 8.1 337.03 448.75 Tm (\012%)Tj /F2 1 Tf 9 0 0 9 365.38 448.75 Tm ( takes four inputsthe first)Tj -26.5978 -1.4444 TD (word and the remaining words, plus their probabilitiesand combines them by append-)Tj T* (ing the first word to the remaining words, and by multiplying the probabilitiesexcept)Tj T* [(that)-254.1(in)-254.3(order)-254.4(to)-254.3(solve)-254.4(problem)-253.7(\(2\),)-254.7(we)-253.9(introduce)-254.2(the)-254.9(third)-254.1(difference:)-255.1(we)-253.9(add)-253.5(logarithms)-254.6(of)]TJ T* (probabilities instead of multiplying the raw probabilities.)Tj 0 -2 TD (Here is the code for)Tj /F8 1 Tf 8.1 0 0 8.1 206.35 378.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 238.75 378.75 Tm (:)Tj /F8 1 Tf 8 0 0 8 138 361.42 Tm (\012 \012 \012$ ")Tj 0 -2.5 TD (9\012\012)Tj 0 -1.25 TD ()Tj /F13 1 Tf 2 0 TD ()Tj /F8 1 Tf 4 0 TD (102 $8/4\(-,43:)Tj -6 -1.25 TD ( ;# 1 1732 732 7 7 % \012 0: 2 56)Tj T* ( / 5\012%1"1 712 $8332 2 \0121\0122 33)Tj T* ( 2\012 $1036)Tj T* ( \012013)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 3.5 0 TD (1 2 2 1 \0122 \01233:)Tj -5.5 -1.25 TD ( ;\012% \012 1$%%2 73 $ = \0122 56=\012)Tj 8.1 0 0 8.1 126 225.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 158.4 225.75 Tm ( makes O\()Tj /F6 1 Tf 4.5367 0 TD (nL)Tj /F2 1 Tf 1.1122 0 TD (\) recursive calls, and each one considers O\()Tj /F6 1 Tf 19.1878 0 TD (L)Tj /F2 1 Tf 0.5567 0 TD (\) splits, so the whole)Tj -28.9933 -1.4444 TD (algorithm is O\()Tj /F6 1 Tf 6.7044 0 TD (nL)Tj /F2 1 Tf 6 0 0 6 196.34 215.78 Tm (2)Tj 9 0 0 9 199.68 212.75 Tm (\). In effect this is the)Tj /F6 1 Tf 9.4067 0 TD (Viterbi)Tj /F2 1 Tf 2.7233 0 TD ( algorithm, with)Tj /F8 1 Tf 8.1 0 0 8.1 376.19 212.75 Tm (\012\012)Tj /F2 1 Tf 9 0 0 9 392.39 212.75 Tm ( implicitly creating the)Tj -29.5989 -1.4444 TD (Viterbi tables.)Tj /F8 1 Tf 8.1 0 0 8.1 126 181.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 158.4 181.75 Tm ( correctly segments the sit down example, and gets right all the examples that)Tj -3.6 -1.4444 TD (the first version got right. Neither version gets the unregarded example right.)Tj 0 -2 TD [(Could)-234.2(we)-233.9(improve)-233.7(on)-234.1(this)-233.4(performance?)-234.2(Probably.)-234.2(We)-234.4(could)-233.9(create)-234(a)-233.3(more)-234.8(accurate)-233.4(model)]TJ 0 -1.4444 TD (of unknown words. We could incorporate more data, and either keep more entries from)Tj T* (the unigram or bigram data, or perhaps add trigram data.)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 227 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 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53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 38.01 54.245 c h 37.995 53.76 m 35.511 53.76 33.495 51.744 33.495 49.26 c 33.495 46.776 35.511 44.76 37.995 44.76 c 40.479 44.76 42.495 46.776 42.495 49.26 c 42.495 51.744 40.479 53.76 37.995 53.76 c h 37.995 53.245 m 35.787 53.245 33.995 51.453 33.995 49.245 c 33.995 47.037 35.787 45.245 37.995 45.245 c 40.203 45.245 41.995 47.037 41.995 49.245 c 41.995 51.453 40.203 53.245 37.995 53.245 c h 38.01 52.745 m 36.078 52.745 34.51 51.177 34.51 49.245 c 34.51 47.313 36.078 45.745 38.01 45.745 c 39.942 45.745 41.51 47.313 41.51 49.245 c 41.51 51.177 39.942 52.745 38.01 52.745 c h 37.995 52.26 m 36.339 52.26 34.995 50.916 34.995 49.26 c 34.995 47.604 36.339 46.26 37.995 46.26 c 39.651 46.26 40.995 47.604 40.995 49.26 c 40.995 50.916 39.651 52.26 37.995 52.26 c h 37.995 51.745 m 36.615 51.745 35.495 50.625 35.495 49.245 c 35.495 47.865 36.615 46.745 37.995 46.745 c 39.375 46.745 40.495 47.865 40.495 49.245 c 40.495 50.625 39.375 51.745 37.995 51.745 c h 38.01 51.245 m 36.906 51.245 36.01 50.349 36.01 49.245 c 36.01 48.141 36.906 47.245 38.01 47.245 c 39.114 47.245 40.01 48.141 40.01 49.245 c 40.01 50.349 39.114 51.245 38.01 51.245 c h 37.995 50.76 m 37.167 50.76 36.495 50.088 36.495 49.26 c 36.495 48.432 37.167 47.76 37.995 47.76 c 38.823 47.76 39.495 48.432 39.495 49.26 c 39.495 50.088 38.823 50.76 37.995 50.76 c h 37.995 50.245 m 37.443 50.245 36.995 49.797 36.995 49.245 c 36.995 48.693 37.443 48.245 37.995 48.245 c 38.547 48.245 38.995 48.693 38.995 49.245 c 38.995 49.797 38.547 50.245 37.995 50.245 c h 38.01 49.745 m 37.734 49.745 37.51 49.521 37.51 49.245 c 37.51 48.969 37.734 48.745 38.01 48.745 c 38.286 48.745 38.51 48.969 38.51 49.245 c 38.51 49.521 38.286 49.745 38.01 49.745 c s 574 49.25 m 574 57.26 l 569.578 57.26 565.99 53.672 565.99 49.25 c 565.99 44.828 569.578 41.24 574 41.24 c 578.422 41.24 582.01 44.828 582.01 49.25 c 582.01 53.672 578.422 57.26 574 57.26 c f 573.99 57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 42 0 obj > /ExtGState > >> endobj 44 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (228)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F1 1 Tf 15 0 0 15 126 674.75 Tm 0 Tc [(Secr)-19(et Codes)]TJ /F2 1 Tf 9 0 0 9 126 655.75 Tm (Our second challenge is to decode a message written in a secret code. Well look at)Tj /F6 1 Tf 0 -1.4445 TD (substitution ciphers)Tj /F2 1 Tf 7.7 0 TD (, in which each letter is replaced by another. The description of what)Tj -7.7 -1.4444 TD [(replaces)-255.1(what)-255.4(is)-255.2(called)-254(the)]TJ /F6 1 Tf 11.7578 0 TD (key)Tj /F2 1 Tf 1.3322 0 TD [(,)-255.3(which)-255.4(we)-255(can)-255(represent)-255.2(as)-254.3(a)-255.6(string)-254.4(of)-255.7(26)-254.7(letters;)-255.5(the)-254.9(first)-254.9(let-)]TJ -13.09 -1.4444 TD (ter replaces a, the second replaces b, and so on. Here is the function to encode a mes-)Tj T* (sage with a substitution cipher key \(the Python library functions)Tj /F8 1 Tf 8.1 0 0 8.1 386.36 603.75 Tm (\012!)Tj /F2 1 Tf 9 0 0 9 422.81 603.75 Tm ( and)Tj /F8 1 Tf 8.1 0 0 8.1 442.82 603.75 Tm ()Tj /F2 1 Tf 9 0 0 9 126 590.75 Tm (do most of the work\):)Tj /F8 1 Tf 8 0 0 8 138 571.42 Tm ()Tj /F13 1 Tf 2 0 TD ()Tj /F8 1 Tf 3 0 TD (1\0122 !3:)Tj -5 -1.25 TD ( ;B \012 7 % $ \0121!11$%32 1!333)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD ()Tj /F8 1 Tf 1 0 TD [(103: 0$$1)-166.4(3 = 071)-166.4(3)]TJ /F13 1 Tf -3 -2.5 TD ()Tj /F8 1 Tf 4 0 TD ( / 4%H!\012$870E4)Tj /F2 1 Tf 9 0 0 9 126 493.75 Tm (Perhaps the simplest of all codes is the)Tj /F6 1 Tf 17.2633 0 TD (shift cipher)Tj /F2 1 Tf 4.42 0 TD (, a substitution cipher in which each let-)Tj -21.6833 -1.4444 TD [(ter)-273.5(in)-274.3(the)-273.8(message)-274(is)-274.1(replaced)-273.6(by)-274.9(the)-273.8(letter)]TJ /F6 1 Tf 18.9278 0 TD (n)Tj /F2 1 Tf 0.83 0 TD [(letters)-274.6(later)-273.3(in)-274.3(the)-273.8(alphabet.)-273.6(If)]TJ /F6 1 Tf 13.4389 0 TD (n)Tj /F2 1 Tf 0.83 0 TD [(=)-274.4(1)0(,)-273.8(then)-273.9(a)]TJ -34.0267 -1.4444 TD (is replaced by b and b is replaced by c, up to z, which is replaced by a. Shift)Tj T* (ciphers are also called)Tj /F6 1 Tf 9.9467 0 TD (Caesar ciphers)Tj /F2 1 Tf 5.6978 0 TD (; they were state-of-the-art in 50 BC. The function)Tj /F8 1 Tf 8.1 0 0 8.1 126 441.75 Tm ()Tj /F2 1 Tf 9 0 0 9 146.25 441.75 Tm ( encodes with a shift cipher:)Tj /F8 1 Tf 8 0 0 8 138 422.42 Tm ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 2.5 0 TD (1\0122 /"3:)Tj -4.5 -1.25 TD ( ;B \012 7 13 $ 1\0122 $%5:6=$%5:63)Tj /F2 1 Tf 9 0 0 9 126 384.75 Tm (We use the function like this:)Tj /F8 1 Tf 8 0 0 8 138 365.42 Tm (,,, 14>2 7 !7 I43)Tj T* (4J82 % % H % 0%H $I4)Tj 0 -2.5 TD (,,, 14K\015> ' 0E42 "3)Tj 0 -1.25 TD (4? ' E4)Tj /F2 1 Tf 9 0 0 9 126 307.75 Tm (To decode a message without knowing the key, we follow the same methodology we did)Tj 0 -1.4444 TD (with segmentations: define a model \(well stick with unigram word probabilities\), enu-)Tj T* (merate candidates, and choose the most probable. There are only 26 candidate shifts to)Tj T* (consider, so we can try them all.)Tj 0 -2.2222 TD (To implement this we define)Tj /F8 1 Tf 8.1 0 0 8.1 243.18 248.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 279.63 248.75 Tm (, which is like)Tj /F8 1 Tf 8.1 0 0 8.1 337.48 248.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 361.78 248.75 Tm (, but returns the log of the)Tj -26.1978 -1.4444 TD (probability, and accepts the input as either a long string of words or a list of words:)Tj /F8 1 Tf 8 0 0 8 138 216.42 Tm ()Tj /F13 1 Tf 2 0 TD (\012\015)Tj /F8 1 Tf 4.5 0 TD (173:)Tj -6.5 -1.25 TD ( ;& *8 ? $%% 7 172 3: 7 / 7173)Tj T* ( \0121"1 71733 7 73)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD (\015)Tj /F8 1 Tf 4 0 TD (103:)Tj -6 -1.25 TD ( ;# $% 7 02 7 145GE6=42 071)-166.6(33)]TJ /F2 1 Tf 9 0 0 9 126 128.75 Tm (Now we can decode by enumerating all candidates and picking the most probable:)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 228 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 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720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 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38.01 51.245 m 36.906 51.245 36.01 50.349 36.01 49.245 c 36.01 48.141 36.906 47.245 38.01 47.245 c 39.114 47.245 40.01 48.141 40.01 49.245 c 40.01 50.349 39.114 51.245 38.01 51.245 c h 37.995 50.76 m 37.167 50.76 36.495 50.088 36.495 49.26 c 36.495 48.432 37.167 47.76 37.995 47.76 c 38.823 47.76 39.495 48.432 39.495 49.26 c 39.495 50.088 38.823 50.76 37.995 50.76 c h 37.995 50.245 m 37.443 50.245 36.995 49.797 36.995 49.245 c 36.995 48.693 37.443 48.245 37.995 48.245 c 38.547 48.245 38.995 48.693 38.995 49.245 c 38.995 49.797 38.547 50.245 37.995 50.245 c h 38.01 49.745 m 37.734 49.745 37.51 49.521 37.51 49.245 c 37.51 48.969 37.734 48.745 38.01 48.745 c 38.286 48.745 38.51 48.969 38.51 49.245 c 38.51 49.521 38.286 49.745 38.01 49.745 c s 574 49.25 m 574 57.26 l 569.578 57.26 565.99 53.672 565.99 49.25 c 565.99 44.828 569.578 41.24 574 41.24 c 578.422 41.24 582.01 44.828 582.01 49.25 c 582.01 53.672 578.422 57.26 574 57.26 c f 573.99 57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 45 0 obj > /ExtGState > >> endobj 47 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (229)Tj /F8 1 Tf 8 0 0 8 138 679.42 Tm ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 6 0 TD (1\0123:)Tj -8 -1.25 TD ( ;L % \012 7 $ / 51\0122 3 11$%336)Tj T* ( \012012 !/ 73)Tj /F2 1 Tf 9 0 0 9 126 631.75 Tm (We can test to see that this works:)Tj /F8 1 Tf 8 0 0 8 138 612.42 Tm (,,, @14J82 % % H % 0%H $I43)Tj T* (4>2 7 !7 I4)Tj /F2 1 Tf 9 0 0 9 126 584.75 Tm (This is all too easy. To see why, look at the 26 candidates, with their log-probabilities:)Tj /F8 1 Tf 8 0 0 8 138 565.42 Tm (J82 % % H % 0%H $I G)Tj T* (M7%2 \012 !% %! I G)Tj T* (\01502 H $ E $ I G)Tj T* (?H2 ! \012H H \012 HI G)Tj T* (EH!82 $ ! ! % H88!I G)Tj T* (N!72 8 \012 !7H7I G'")Tj T* (B%\01202 7 $\012 \012 $ 08!0\012I G)Tj T* (L\0122 0 \0127I G)Tj T* (OE2 H H$ 8 H H 8 E0\012EI G)Tj T* (K$H2 E! ! 7H$ $! H! 7 $I G')Tj T* ($%!2 8 0! ! 0 $%E%I G)Tj T* (P2 %\012 7\012 \012 \012 $I G)Tj T* (+\0122 0 8E\012 H\0128 E %I G')Tj T* (>2 7 !7 I G)Tj T* (H2 $ E$8 0% $ $0 % I G')Tj T* (*!8$2 7 $8 8 \012$ 8I G)Tj T* (Q872 %0 E7 7 E 87I G)Tj T* ( \012702 0 0 780I G)Tj T* (R0H2 E % $% 0H7HI G)Tj T* (#E!2 H E E !0!EI G)Tj T* (-$E2 !8 8% 8 8 EHI G)Tj T* (&%\01282 7 7 8% %7 87 \012!E\012%I G)Tj T* (\)%72 \0120 0 H7 0 70 H %I G')Tj T* (S02 !0 0 ! \012%I G)Tj T* (T$2 E HE E 8E $$I G'")Tj T* (UE2 $ ! \012E 7E \012 I G)Tj /F2 1 Tf 9 0 0 9 126 297.75 Tm [(As)-252.3(you)-252.7(scan)-253.8(the)-252.7(list,)-252.9(exactly)-252(one)-253(line)-253(stands)-252(out)-253.3(as)-253.2(English-like,)-251.8(and)]TJ /F8 1 Tf 8.1 0 0 8.1 395.26 297.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 421.84 297.75 Tm [(agrees)-252(with)-253(our)]TJ -32.8711 -1.4444 TD [(intuition,)-264.1(giving)-264.9(that)-265.2(line)-264.1(a)-265.6(log-probability)-264.6(of)-264.6(25)-264.7(\(that)-264(is,)-265(10)]TJ 6 0 0 6 366.03 287.78 Tm (25)Tj 9 0 0 9 375.7 284.75 Tm [(\),)-265.2(which)-264.3(is)-264.1(10)]TJ 6 0 0 6 429.69 287.78 Tm (50)Tj 9 0 0 9 438.75 284.75 Tm [(times)-264.2(more)]TJ -34.75 -1.4444 TD (probable than any other candidate.)Tj 0 -2.2222 TD (The code maker can make the code breakers job harder by eliminating punctuation,)Tj 0 -1.4444 TD (spaces between words, and uppercase distinctions. That way the code breaker doesnt get)Tj T* (clues from short words like I, a, and the, nor from guessing that the character after)Tj T* (an apostrophe should be s or t. Heres an encryption scheme,)Tj /F8 1 Tf 8.1 0 0 8.1 388.69 212.75 Tm ()Tj /F2 1 Tf 9 0 0 9 412.99 212.75 Tm (, that removes)Tj -31.8878 -1.4444 TD (nonletters, converts everything to lowercase, and then applies a shift cipher:)Tj /F8 1 Tf 8 0 0 8 138 180.42 Tm ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 3 0 TD (1\0122 /"3:)Tj -5 -1.25 TD ( ;B 7 13 $2 5GE6 1H@1\01232 3)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD (\015)Tj /F8 1 Tf 6 0 TD (103:)Tj -8 -1.25 TD ( ;>7 0 \0128 0$ 5GE6 %145VGE642 442 071)-166.6(33)]TJ ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 229 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 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576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 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40.203 45.245 41.995 47.037 41.995 49.245 c 41.995 51.453 40.203 53.245 37.995 53.245 c h 38.01 52.745 m 36.078 52.745 34.51 51.177 34.51 49.245 c 34.51 47.313 36.078 45.745 38.01 45.745 c 39.942 45.745 41.51 47.313 41.51 49.245 c 41.51 51.177 39.942 52.745 38.01 52.745 c h 37.995 52.26 m 36.339 52.26 34.995 50.916 34.995 49.26 c 34.995 47.604 36.339 46.26 37.995 46.26 c 39.651 46.26 40.995 47.604 40.995 49.26 c 40.995 50.916 39.651 52.26 37.995 52.26 c h 37.995 51.745 m 36.615 51.745 35.495 50.625 35.495 49.245 c 35.495 47.865 36.615 46.745 37.995 46.745 c 39.375 46.745 40.495 47.865 40.495 49.245 c 40.495 50.625 39.375 51.745 37.995 51.745 c h 38.01 51.245 m 36.906 51.245 36.01 50.349 36.01 49.245 c 36.01 48.141 36.906 47.245 38.01 47.245 c 39.114 47.245 40.01 48.141 40.01 49.245 c 40.01 50.349 39.114 51.245 38.01 51.245 c h 37.995 50.76 m 37.167 50.76 36.495 50.088 36.495 49.26 c 36.495 48.432 37.167 47.76 37.995 47.76 c 38.823 47.76 39.495 48.432 39.495 49.26 c 39.495 50.088 38.823 50.76 37.995 50.76 c h 37.995 50.245 m 37.443 50.245 36.995 49.797 36.995 49.245 c 36.995 48.693 37.443 48.245 37.995 48.245 c 38.547 48.245 38.995 48.693 38.995 49.245 c 38.995 49.797 38.547 50.245 37.995 50.245 c h 38.01 49.745 m 37.734 49.745 37.51 49.521 37.51 49.245 c 37.51 48.969 37.734 48.745 38.01 48.745 c 38.286 48.745 38.51 48.969 38.51 49.245 c 38.51 49.521 38.286 49.745 38.01 49.745 c s 574 49.25 m 574 57.26 l 569.578 57.26 565.99 53.672 565.99 49.25 c 565.99 44.828 569.578 41.24 574 41.24 c 578.422 41.24 582.01 44.828 582.01 49.25 c 582.01 53.672 578.422 57.26 574 57.26 c f 573.99 57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 48 0 obj > /ExtGState > >> endobj 52 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (230)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 126 678.75 Tm 0 Tc [(And)-235.4(heres)-236.3(a)-235.6(way)-235.8(to)-236.6(break)-235.8(this)-235.7(code)-236.2(by)-236(enumerating)-235.6(each)-236.1(candidate,)-235.1(segmenting)-235.5(each)-236.1(one,)]TJ 0 -1.4444 TD (and choosing the one with the highest probability:)Tj /F8 1 Tf 8 0 0 8 138 646.42 Tm ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 6.5 0 TD (1\0123:)Tj -8.5 -1.25 TD ( ;N \012 7 $2 7 $ / 5\01211\0122 33 11$%336)Tj T* ( $2 7 / \012013)Tj T* ( 4 4173)Tj /F2 1 Tf 9 0 0 9 126 588.75 Tm (Lets see how well it works:)Tj /F8 1 Tf 8 0 0 8 138 569.42 Tm (,,, 14>2 7 !7 I43)Tj T* (48%%H%0%H$4)Tj 0 -2.5 TD (,,, @148%%H%0%H$43)Tj 0 -1.25 TD (4 7 !7 4)Tj 0 -2.5 TD (,,, @114#%433)Tj 0 -1.25 TD (4%4)Tj 0 -2.5 TD (,,, @11; I;33)Tj 0 -1.25 TD (4 4)Tj 0 -2.5 TD (,,, @11;T4 2 +I;33)Tj 0 -1.25 TD (47 !4)Tj 0 -2.5 TD (,,, \012 / 4O +%: J 2 8 \012 )Tj 0 -1.25 TD (TW 7 % $ \012 B\012$@11\01233)Tj 0 -1.25 TD (4 !% 8 \012 7 7 )Tj T* (% $ \012 \012$4)Tj /F2 1 Tf 9 0 0 9 126 351.75 Tm (Still way too easy. Lets move on to a general substitution cipher, in which any letter can)Tj 0 -1.4444 TD (be substituted for any other. Now we can no longer enumerate the possibilities, because)Tj T* (there are 26! keys \(about 4)Tj /F11 1 Tf 12.1856 0 TD ()Tj /F2 1 Tf 0.7156 0 TD (10)Tj 6 0 0 6 252.12 328.78 Tm (26)Tj 9 0 0 9 258.79 325.75 Tm (\), rather than just 26.)Tj /F6 1 Tf 9.8344 0 TD (The Code Book)Tj /F2 1 Tf 5.8889 0 TD ( by Simon Singh)Tj -30.4778 -1.4444 TD (\(Anchor\) offers five strategies \(and well mention a sixth\) for breaking ciphers:)Tj 0.5111 -2.2222 TD [(1.)-654.9(Letter)-265.6(unigram)-266.3(frequencies.)-265.6(Match)-265.8(common)-265.9(letters)-265.8(in)-266.6(the)-266(message)-265.1(to)-266.6(common)-265.9(letters)]TJ 1.4889 -1.4444 TD (in English \(like e\) and uncommon to uncommon \(like z\).)Tj -1.4889 -1.8889 TD [(2.)-654.9(Double letter analysis. A double in the coded message is still double in the decoded)]TJ 1.4889 -1.4444 TD (message. Consider the least and most common double letters.)Tj -1.4889 -1.8889 TD [(3.)-654.9(Look for common words like the, and, and of. One-letter words are most often)]TJ 1.4889 -1.4444 TD (a or I.)Tj -1.4889 -1.8889 TD [(4.)-654.9(If possible, get a frequency table made up of the type of messages you are dealing)]TJ 1.4889 -1.4444 TD (with. Military messages use military jargon, etc.)Tj -1.4889 -1.8889 TD [(5.)-654.9(Guess a word or phrase. For example, if you can guess that the message will contain)]TJ 1.4889 -1.4444 TD (your faithful servant, try it.)Tj -1.4889 -1.8889 TD [(6.)-654.9(Use word patterns. For example, the coded word abbccddedf is very likely)]TJ 1.4889 -1.4444 TD (bookkeeper, because there are no other words in the corpus with that pattern.)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 230 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 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f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 53 0 obj > /ExtGState > >> endobj 55 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (231)Tj /F2 1 Tf 9 0 0 9 126 678.75 Tm (For messages that do not contain spaces between words, strategies 3 and 6 do not apply.)Tj 0 -1.4444 TD (Strategies 1 and 2 contain only 26 probabilities each, and seem targeted for a human ana-)Tj T* [(lyst)-256.3(with)-256.3(limited)-256.8(memory)-256.4(and)-257.4(computing)-256.3(power,)-256(not)-256.7(for)-256.7(a)-256.7(computer)-256.3(program.)-257.3(Strategies)-256.4(4)]TJ T* (and 5 are for special-purpose, not general-purpose, decoders. It looks like were on our)Tj T* (own in coming up with a strategy. But we know the methodology.)Tj /F10 1 Tf 0 -2.2222 TD [(I.)-259.8(Define)-259.2(a)-259.6(probabilistic)-259.7(model:)]TJ /F2 1 Tf 15.4967 0 TD [(We)-258.9(could)-259.4(evaluate)-259.9(candidates)-259.6(the)-259.3(same)-259.6(way)-259.1(we)-259.4(did)-260(for)]TJ -15.4967 -1.4444 TD (shift ciphers: segment the text and calculate the probability of the words. But considering)Tj T* (step II of the methodology, our first few candidates \(or few thousand\) will likely be very)Tj T* [(poor)-244.1(ones.)-243.8(At)-243.9(the)-243.8(start)-243.8(of)-243.4(our)-244(exploration,)-244.5(we)-243.9(wont)-243.6(have)-244.2(anything)-243.4(resembling)-243.3(words,)-244.7(so)-243.9(it)]TJ T* [(wont)-253.6(do)-253.5(much)-252.6(good)-254.2(to)-253.2(try)-253.2(to)-253.2(segment.)-253.2(However,)-254.1(we)-252.8(may)-253.9(\(just)-253.3(by)-253.8(accident\))-252.7(have)-254.2(decoded)]TJ T* [(a)-268.9(few)-270(letters)-269.1(in)-268.8(a)-268.9(row)-270(that)-268.5(make)-269.3(sense.)-269.6(So)-269.1(lets)-268.7(use)]TJ /F6 1 Tf 22.51 0 TD [(letter)-241.2(n-grams)]TJ /F2 1 Tf 5.8456 0 TD [(rather)-269.1(than)-269.4(words)-269.4(for)-268.9(our)]TJ -28.3556 -1.4444 TD (language model. Should we look at letter bigrams? 3-grams? 5-grams? I chose 3-grams)Tj T* (because they are the shortest that can represent common short words \(strategy 3\). I cre-)Tj T* (ated the datafile)Tj /F8 1 Tf 8.1 0 0 8.1 192.84 502.75 Tm (@)Tj /F2 1 Tf 9 0 0 9 225.24 502.75 Tm ( by counting the letter 3-grams \(with spaces and punctuation)Tj -11.0267 -1.4444 TD (removed\) within the word bigram datafiles \(I couldnt just look at the vocabulary file,)Tj T* (because I need to consider letter trigrams that cross word boundaries\). All of the 26)Tj 6 0 0 6 459.38 479.78 Tm (3)Tj 9 0 0 9 462.71 476.75 Tm ( =)Tj -37.4122 -1.4444 TD (17,576 trigrams appear. Here are the top and bottom 10:)Tj /F8 1 Tf 8 0 0 8 138 444.42 Tm ( X E X)Tj 0 -1.25 TD ( ""X H8 X)Tj T* ( "X H X)Tj T* ( "X E X)Tj T* ( ""X H0 X)Tj T* ( "X H7 X)Tj T* ( X H X)Tj T* ( X E X)Tj T* ( X HE X)Tj T* ( X E X)Tj /F2 1 Tf 9 0 0 9 126 336.75 Tm (The letter trigram probability is computed like this:)Tj /F8 1 Tf 8 0 0 8 138 317.42 Tm ()Tj /F13 1 Tf 2 0 TD (\012\015)Tj /F8 1 Tf 6 0 TD (103:)Tj -8 -1.25 TD ( ;& G$%% 0 G\012 \012 \0121"1 133 \012102 33)Tj 0 -2.5 TD ( / 114@433)Tj 0 -1.25 TD ( / 114@433 DD T4 )Tj /F10 1 Tf 9 0 0 9 126 249.75 Tm (II. Enumerate candidates:)Tj /F2 1 Tf 12.8022 0 TD ( We cant consider all 4)Tj /F11 1 Tf 10.5567 0 TD ()Tj /F2 1 Tf 0.7156 0 TD (10)Tj 6 0 0 6 352.67 252.78 Tm (26)Tj 9 0 0 9 359.35 249.75 Tm ( possible keys, and there does)Tj -25.9278 -1.4444 TD [(not)-270(appear)-271.2(to)-269.9(be)-269.7(a)-271.1(way)-270.2(to)-269.9(systematically)-270.4(eliminate)-270.6(nonoptimal)-269.6(candidates,)-270.5(as)-271(there)-270.3(was)-270.4(in)]TJ T* (segmentation. That suggests a)Tj /F6 1 Tf 13.5 0 TD (local search)Tj /F2 1 Tf 4.5856 0 TD ( strategy, such as)Tj /F6 1 Tf 7.8156 0 TD (hill climbing)Tj /F2 1 Tf 5.0856 0 TD (. Suppose you)Tj -30.9867 -1.4444 TD (wanted to reach maximum elevation, but had no map. With the hill-climbing strategy,)Tj T* (you would start at a random location,)Tj /F6 1 Tf 17.0767 0 TD (x)Tj /F2 1 Tf 0.4444 0 TD (, and take a step to a neighboring location. If that)Tj -17.5211 -1.4444 TD [(location)-236.2(is)-235.2(higher,)-236.3(continue)-234.9(to)-236.5(hill-climb)-235.4(from)-235.3(there.)-235.6(If)-236.3(not,)-235.3(consider)-235.9(another)-235.5(neighbor)-235.7(of)]TJ /F6 1 Tf 39.0422 0 TD (x)Tj /F2 1 Tf 0.4444 0 TD (.)Tj -39.4867 -1.4444 TD (Of course, if you start at a random location on Earth and start walking uphill, you proba-)Tj T* (bly wont end up on top of Mt. Everest. More likely youll end up on top of a small local)Tj T* (hill, or get stuck wandering around a flat plain. Therefore we add)Tj /F6 1 Tf 29.3233 0 TD (random restarts)Tj /F2 1 Tf 6.3078 0 TD ( to our)Tj -35.6311 -1.4444 TD (hill-climbing algorithm: after weve taken a certain number of steps, we start all over)Tj T* (again in a new random location.)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 231 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 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62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 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49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 56 0 obj > /ExtGState > >> endobj 58 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (232)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 126 678.75 Tm 0 Tc [(Here)-276.8(is)-277.4(the)-276(general)]TJ /F8 1 Tf 8.1 0 0 8.1 203.47 678.75 Tm (\012%)Tj /F2 1 Tf 9 0 0 9 242.41 678.75 Tm [(algorithm.)-276.7(It)-276.1(takes)-277.5(a)-276.7(starting)-277(location,)]TJ /F6 1 Tf 16.8811 0 TD (x)Tj /F2 1 Tf 0.4444 0 TD [(,)-276.4(a)-277.8(function)]TJ /F8 1 Tf 8.1 0 0 8.1 446.65 678.75 Tm ()Tj /F2 1 Tf 9 0 0 9 453.19 678.75 Tm [(that)-276.3(we)]TJ -36.3544 -1.4444 TD [(are)-264.3(trying)-265.3(to)-264.3(optimize,)-264.5(a)-264.4(function)]TJ /F8 1 Tf 8.1 0 0 8.1 259.95 665.75 Tm (%)Tj /F2 1 Tf 9 0 0 9 298.78 665.75 Tm [(that)-264.1(generates)-264.6(the)-264.9(neighbors)-264.5(of)-264.5(a)-264.4(location,)-264.9(and)]TJ -19.1978 -1.4444 TD (a maximum number of steps to take. \(If the variable)Tj /F8 1 Tf 8.1 0 0 8.1 337.66 652.75 Tm (%)Tj /F2 1 Tf 9 0 0 9 374.11 652.75 Tm ( is true, it prints the best)Tj /F6 1 Tf 11.0944 0 TD (x)Tj /F2 1 Tf -38.6622 -1.4444 TD (and its score.\))Tj /F8 1 Tf 8 0 0 8 138 620.42 Tm ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 4.5 0 TD (102 2 %2 $/"3:)Tj -6.5 -1.25 TD ( ;- 0 \0120\012E 1032 %1030 / 103)Tj T* ( % / 1%1033)Tj T* ( 1$3:)Tj T* [( 0 / %01)-166.5(3)]TJ T* ( 0 / 103)Tj T* ( 0 , 0:)Tj T* ( 02 0 / 02 0)Tj T* ( % / 1%1033)Tj T* ( %: $ 4\012%:42 02 103)Tj T* ( 0)Tj 0 -2.5 TD (% / L)Tj /F2 1 Tf 9 0 0 9 126 472.75 Tm [(To)-258(use)]TJ /F8 1 Tf 8.1 0 0 8.1 154.15 472.75 Tm (\012%)Tj /F2 1 Tf 9 0 0 9 192.93 472.75 Tm [(for)-257.8(decoding,)-258.7(we)-257.2(need)-258.5(to)-257.7(specify)-258.8(the)-258.2(parameters.)-257.9(The)-257.4(locations)-258.3(we)-258.3(will)-257.7(be)]TJ -7.4367 -1.4444 TD (searching through will be plain-text \(decoded\) messages. We will attempt to maximize)Tj T* (their letter trigram frequency, so)Tj /F8 1 Tf 8.1 0 0 8.1 259.17 446.75 Tm ()Tj /F2 1 Tf 9 0 0 9 263.22 446.75 Tm ( will be)Tj /F8 1 Tf 8.1 0 0 8.1 294.9 446.75 Tm ( )Tj /F2 1 Tf 9 0 0 9 343.5 446.75 Tm (. Well start with)Tj /F6 1 Tf 7.7056 0 TD (x)Tj /F2 1 Tf 0.4433 0 TD ( being the mes-)Tj -32.3156 -1.4444 TD [(sage)-255.4(decrypted)-255.6(with)-255.2(a)-255.6(random)-255.5(key.)-255.7(Well)-254.9(do)-255.8(random)-255.5(restarts,)-255.5(but)-255.7(when)-255.2(we)-255(gather)-255.9(the)-254.9(can-)]TJ T* [(didates)-236.9(from)-236.4(each)-237.2(restart,)-236.7(we)-236.1(will)-237.6(choose)-236.2(the)-237.1(one)-236.3(best)-236.5(according)-236.4(to)]TJ /F8 1 Tf 8.1 0 0 8.1 389.92 420.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 422.32 420.75 Tm [(,)-236.4(rather)-236.9(than)-236.1(by)]TJ /F8 1 Tf 8.1 0 0 8.1 126 407.75 Tm ( )Tj /F2 1 Tf 9 0 0 9 174.6 407.75 Tm (:)Tj /F8 1 Tf 8 0 0 8 138 388.42 Tm ()Tj /F13 1 Tf 2 0 TD ()Tj /F8 1 Tf 6 0 TD (1\0122 $/2 /3:)Tj -8 -1.25 TD ( ;N % $ 7 \012 \012% / 171\01233)Tj T* ( / 5\012%11\0122 !/11$%3332)Tj T* ( 2 %@\0122 $3)Tj T* ( @ 136)Tj T* ( $2 7 / \01201\01213 3)Tj T* ( 4 4173)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD ()Tj /F8 1 Tf 4 0 TD (13:)Tj -6 -1.25 TD ( ;# \012 $ $ / 13)Tj T* ( \01213)Tj T* ( )Tj /F13 1 Tf 0 -2.5 TD ()Tj /F8 1 Tf 1.5 0 TD ( / 44)Tj /F2 1 Tf 9 0 0 9 126 220.75 Tm (Now we need to define)Tj /F8 1 Tf 8.1 0 0 8.1 221.53 220.75 Tm (%@\012)Tj /F2 1 Tf 9 0 0 9 286.33 220.75 Tm (, which generates decryptions of the message to)Tj -17.8144 -1.4444 TD (try next. We first try to repair improbable letter bigrams. For example, the least frequent)Tj T* (bigram, jq, has probability 0.0001%, which is 50,000 times less than the most probable)Tj T* [(bigrams,)-273.2(in)-274.1(and)-273(th.)-273.3(So)-273.6(if)-273.7(we)-273.9(see)-273.2(a)-273.3(jq)-273.5(in)]TJ /F8 1 Tf 8.1 0 0 8.1 304.57 181.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 316.72 181.75 Tm [(,)-273.1(w)0(e)-273.9(try)-273.2(swapping)-273.9(the)-273.8(j)-272.9(with)-274.1(each)-272.8(of)-273.4(the)]TJ -21.1911 -1.4444 TD [(other)-268.8(letters,)-268.9(and)-269.7(also)-269.2(try)-268.8(swapping)-268.3(the)-269.3(q.)-269.1(If)-268.6(a)-268.9(swap)-270(yields)-268.6(a)-268.9(more)-269.2(frequent)-268.3(bigram,)-268.9(then)]TJ T* (we generate the message that results from making the swap. After exhausting repairs of)Tj T* (the 20 most improbable bigrams, we consider random swaps:)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 232 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 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569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 59 0 obj > /ExtGState > >> endobj 61 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (233)Tj /F8 1 Tf 8 0 0 8 138 679.42 Tm ()Tj /F13 1 Tf 2 0 TD ( \015 )Tj /F8 1 Tf 8 0 TD (1\0123:)Tj -10 -1.25 TD ( ;O % !2 $ % 7$12%3: \0121!1=%2 %=33)Tj T* ( %\012 $\01212 1\0121\0122 332 3:)Tj T* ( %"2% / %\012)Tj T* ( $%:)Tj T* ( %"//%:)Tj T* ( 1=3 , 1%\0123: 7$12%"3)Tj T* ( :)Tj T* ( 1=%3 , 1%\0123: 7$12%"3)Tj T* ( 1%"=3 , 1%\0123: 7$12%3)Tj T* ( 7 &:)Tj T* ( 7$1\0121$%32 \0121$%33)Tj /F2 1 Tf 9 0 0 9 126 541.75 Tm 0.0056 Tc [(L)6(ets)-237.7(see)-237.6(how)-237.9(well)-237.8(this)-236.7(performs.)-234.4(Well)-237(try)-237.6(it)-239(on)-238.5(some)-236.9(ciphers)-235.1(from)-237.5(Robert)-236.8(Raynards)-234(book)]TJ /F6 1 Tf 0 -1.4444 TD (Secret Code Breaker)Tj /F2 1 Tf 7.93 0 TD ( \(Smith and Daniel; see)Tj /F6 1 Tf 10.7878 0 TD (http://secretcodebreaker.com)Tj /F2 1 Tf 11.3111 0 TD (\). First a warm-up)Tj -30.0289 -1.4444 TD (message:)Tj /F8 1 Tf 8 0 0 8 138 496.42 Tm 0 Tc (,,, \012 / 4N-N#Q ULPS NJ-? \015*R\015> &\015U S?N? O\015--\015 R#& OOUP &R P-? \015R N#)Tj 0 -1.25 TD (-N- N\)\015? R- \015RN#- N#P* -?\015O J&J \015-?- RU+- OU #-#R \015QO\015 -P \015-)Tj T* (\015RKN \015-?\015+ ON- \015T-P* N+? \015RK\015# #J\015B4)Tj 0 -2.5 TD (,,, @%1\0123)Tj 0 -1.25 TD (4 % !7 7 8)Tj T* ( $ % \012 )Tj T* ($ 0 $ \012 H4)Tj /F2 1 Tf 9 0 0 9 126 408.75 Tm (This is correct except that crypt analysts should be one word. \(It isnt in)Tj /F8 1 Tf 8.1 0 0 8.1 422.36 408.75 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 430.46 408.75 Tm (, but it is in)Tj -33.8289 -1.4444 TD (the 13-million-word vocabulary.\) Note the last character \(E in the cipher text\) was)Tj T* (added to make the blocks of five letters come out even.)Tj 0 -2.2222 TD (Now an actual message from Baron August Schluga, a German spy in World War I:)Tj /F8 1 Tf 8 0 0 8 138 343.42 Tm (,,, \012 / 4*+NL -B#>P ?L+ L+N>S *R?# K>P\) +L&L> +-&B* JR*NR *&&B? &&B* R>PL-)Tj 0 -1.25 TD (*Q-\) >R&> &B* R*+#B ?&&?# K+>R& B>?R R?-L- +>&> --L\015 *>+?# #>\)+& >P\)+)Tj T* (L&L>+ L+-\) L#L* +#JU?4)Tj 0 -2.5 TD (,,, @%1\0123)Tj 0 -1.25 TD (4 \012$ 8 ! \012 $\012 $$ )Tj T* ( ! $% \012 )Tj T* (74)Tj /F2 1 Tf 9 0 0 9 126 255.75 Tm (Heres a 1992 message from the KGB to former CIA officer Aldrich Ames, who was con-)Tj 0 -1.4444 TD (victed of spying in 1994:)Tj /F8 1 Tf 8 0 0 8 138 223.42 Tm (,,, \012 / 4*>OS RSB>K T&&\015 >BKQ& TBRS B?&R LP* BNL >LJL -RL- *NKRL QB\)&*)Tj 0 -1.25 TD ( & &NR* L-RN &TK&* KK>LP Q>L-N KRLBN KBO*R &TS*R K&*KK >LPTB ??&- &KN&)Tj T* (URRLQ B\)&JL ->LPB NBLN* L-RO *>*O* &&R BNQBN LORL &>U*4)Tj 0 -2.5 TD (,,, @%1\0123)Tj 0 -1.25 TD (4\012 7! % 7 \012 $ \012 8 \012)Tj T* (% 7 $ 7 $ 7 % 0 8 )Tj T* ($ % \012 % 0%4)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 233 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 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742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 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[(This)-251.5(1943)-252.6(message)-251.7(from)-252(German)-252.2(U-Boat)-251.9(command)-251.4(was)-252.7(intercepted)-252.2(and)-251.9(decoded,)-251.7(saving)-251.6(a)]TJ 0 -1.4444 TD (convoy of Allied ships:)Tj /F8 1 Tf 8 0 0 8 138 646.42 Tm (\012 / 4T>P\) PJ?#+ TL L PR-+ T#-- TB & P#?- ?P#\015 ?\015- K?O #TTR -Q -S P)Tj 0 -1.25 TD (?-\)L TLQ& KT?- T?RT L?P#? O > U> -\015PRR PR- #P\015-T >-?>T O?KP)Tj T* (R-T> UTQ>4)Tj 0 -2.5 TD (,,, @%1\0123)Tj 0 -1.25 TD (4 8 ! $ $ \012 $ %7 $ )Tj T* ( % \012 0$ $ \012$ 0 %4)Tj /F2 1 Tf 9 0 0 9 126 568.75 Tm [(This)-247.1(answer)-246(confuses)-246.1(the)-247.1(y)-246.1(and)-247.4(v.)-245.9(A)-246.9(human)-246.8(analyst)-246.4(would)-246.2(realize)-246.5(cony)-246.9(ov)-246.3(should)-246.8(be)]TJ 0 -1.4444 TD (convoy and that therefore point yd should be point vd. Our program never consid-)Tj T* (ered that possibility, because the letter trigram probability of the correct text is less than)Tj T* [(the)-261.5(one)-261.9(shown)-261.3(here.)-262(We)-261.1(could)-261.6(perhaps)-261.2(fix)-262.1(the)-261.6(problem)-261.5(by)-261.5(inventing)-262.1(a)-261.1(better)-261.3(scoring)-261.9(func-)]TJ T* (tion that does not get trapped in a local maximum. Or we could add a second level of hill-)Tj T* (climbing search: take the candidates generated by the first search and do a brief search)Tj T* (with)Tj /F8 1 Tf 8.1 0 0 8.1 146.84 490.75 Tm (\012)Tj /F2 1 Tf 9 0 0 9 179.24 490.75 Tm ( as the scoring function. Well leave that exercise to the reader.)Tj /F1 1 Tf 15 0 0 15 126 461.75 Tm [(Spelling Corr)-19(ection)]TJ /F2 1 Tf 9 0 0 9 126 442.75 Tm (Our final task is spelling correction: given a typed word,)Tj /F6 1 Tf 25.1356 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD (, determine what word)Tj /F6 1 Tf 10.52 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD ( was)Tj -36.7122 -1.4444 TD (most likely intended. For example, if)Tj /F6 1 Tf 16.6344 0 TD (w)Tj /F2 1 Tf 0.7211 0 TD ( is acomodation, c should be accommodation.)Tj -17.3556 -1.4444 TD (\(If)Tj /F6 1 Tf 1.3144 0 TD (w)Tj /F2 1 Tf 0.7211 0 TD ( is the, then)Tj /F6 1 Tf 6.4444 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD ( too should be the.\))Tj -8.8144 -2.2222 TD [(Following)-240.8(the)-240.4(standard)-240.4(methodology,)-240.9(we)-240.6(want)-239.9(to)-241(choose)-240.6(the)]TJ /F6 1 Tf 26.9833 0 TD (c)Tj /F2 1 Tf 0.5744 0 TD [(that)-240.8(maximizes)-240.1(P\()]TJ /F6 1 Tf 7.9233 0 TD (c)Tj /F2 1 Tf 0.5756 0 TD (|)Tj /F6 1 Tf 0.4622 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD [(\).)-239.7(But)]TJ -37.2411 -1.4444 TD (defining this probability is not straightforward. Consider)Tj /F6 1 Tf 25.2289 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( = thew. One candidate)Tj /F6 1 Tf 11.5633 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD ( is)Tj -37.8478 -1.4444 TD [(theits)-263.3(the)-262.7(most)-262.9(common)-262.5(word,)-263.8(and)-263(we)-262.8(can)-262.8(imagine)-262.7(the)-263.8(typists)-262.5(finger)-262.5(slipping)-264(off)-262.9(the)]TJ T* (e key and hitting the w. Another candidate is thawa fairly common word)Tj T* (\(although 30,000 times less frequent than the\), and it is common to substitute one)Tj T* (vowel for another. Other candidates include thew itself \(an obscure term for muscle or)Tj T* (sinew\), threw, and Thwe, a family name. Which should we choose? It seems that we)Tj T* (are conflating two factors: how probable is)Tj /F6 1 Tf 19.1711 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD ( on its own, and how likely is it that)Tj /F6 1 Tf 16.3378 0 TD (w)Tj /F2 1 Tf 0.7211 0 TD ( could)Tj -36.5644 -1.4444 TD [(be)-257.4(a)-256.7(typo)-255.8(for)]TJ /F6 1 Tf 5.8067 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD [(,)-257.6(o)0(r)-256.1(a)-256.7(mispronunciation,)-257.4(or)-256.1(some)-257(other)-257.6(kind)-256.8(of)-256.8(misspelling.)-255.8(One)-257.8(might)-256.6(think)]TJ -6.14 -1.4444 TD [(we)-252.8(will)-252.1(have)-252(to)-253.2(combine)-252.6(these)-252.5(factors)-251.8(in)-253.2(some)-251.4(ad)-252.9(hoc)-252.3(fashion,)-253.1(but)-252.3(it)-252.3(turns)-252.5(out)-252.2(that)-251.9(there)-252.5(is)]TJ T* (a mathematical formula, Bayess theorem, that tells us precisely how to combine them to)Tj T* (find the best candidate:)Tj 1.1111 -2.2222 TD (argmax)Tj /F6 1 Tf 7.2 0 0 7.2 165.99 232.32 Tm (c)Tj /F2 1 Tf 9 0 0 9 170.2 233.75 Tm (P\()Tj /F6 1 Tf 0.9444 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD (\) = argmax)Tj /F6 1 Tf 7.2 0 0 7.2 239.11 232.32 Tm (c)Tj /F2 1 Tf 9 0 0 9 243.32 233.75 Tm (P\()Tj /F6 1 Tf 0.9444 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\) P\()Tj /F6 1 Tf 1.6111 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\))Tj -17.76 -2.4256 TD 0.01 Tc (Here P\()Tj /F6 1 Tf 3.4044 0 TD 0 Tc (c)Tj /F2 1 Tf 0.4367 0 TD 0.01 Tc (\), the probability that)Tj /F6 1 Tf 10.0189 0 TD 0 Tc (c)Tj /F2 1 Tf 0.3433 0 TD 0.01 Tc ( is the intended word, is called the)Tj /F6 1 Tf 15.9111 0 TD (language model)Tj /F2 1 Tf 6.4467 0 TD (, and)Tj -36.5611 -1.4444 TD (P\()Tj /F6 1 Tf 0.9644 0 TD 0 Tc (w)Tj /F2 1 Tf 1.0022 0 TD (|)Tj /F6 1 Tf 0.5011 0 TD (c)Tj /F2 1 Tf 0.4367 0 TD [(\))-10(,)-279.7(the)-260.4(probability)-259.8(that)-259.7(an)-261.2(author)-260(would)-259.5(type)]TJ /F6 1 Tf 19.6311 0 TD (w)Tj /F2 1 Tf 0.9811 0 TD (when)Tj /F6 1 Tf 2.7978 0 TD (c)Tj /F2 1 Tf 0.5944 0 TD [(is)-259.7(intended,)-260.3(is)-259.7(called)-260.7(the)]TJ /F6 1 Tf 10.8567 0 TD (error)Tj -37.7656 -1.4444 TD (model)Tj /F2 1 Tf 2.6533 0 TD (or)Tj /F6 1 Tf 1.2089 0 TD [(noisy)-237.3(channel)-236.5(model)]TJ /F2 1 Tf 8.0889 0 TD [(.)-263.1(\(The)-264(idea)-263.8(is)-264.1(that)-264.1(the)-263.8(ideal)-264.7(author)-263.3(intended)-263.9(to)-264.3(type)]TJ /F6 1 Tf 22.8311 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD [(,)-263.1(but)-264.5(some)]TJ -35.1167 -1.4444 TD (noise or static on the line altered)Tj /F6 1 Tf 14.8356 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD ( to)Tj /F6 1 Tf 1.4456 0 TD (w)Tj /F2 1 Tf 0.7211 0 TD (.\) Unfortunately, we dont have an easy way to)Tj -17.3367 -1.4444 TD (estimate this model from the corpus data we havethe corpus says nothing about what)Tj T* (words are misspellings of others.)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 234 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 38.01 54.245 c h 37.995 53.76 m 35.511 53.76 33.495 51.744 33.495 49.26 c 33.495 46.776 35.511 44.76 37.995 44.76 c 40.479 44.76 42.495 46.776 42.495 49.26 c 42.495 51.744 40.479 53.76 37.995 53.76 c h 37.995 53.245 m 35.787 53.245 33.995 51.453 33.995 49.245 c 33.995 47.037 35.787 45.245 37.995 45.245 c 40.203 45.245 41.995 47.037 41.995 49.245 c 41.995 51.453 40.203 53.245 37.995 53.245 c h 38.01 52.745 m 36.078 52.745 34.51 51.177 34.51 49.245 c 34.51 47.313 36.078 45.745 38.01 45.745 c 39.942 45.745 41.51 47.313 41.51 49.245 c 41.51 51.177 39.942 52.745 38.01 52.745 c h 37.995 52.26 m 36.339 52.26 34.995 50.916 34.995 49.26 c 34.995 47.604 36.339 46.26 37.995 46.26 c 39.651 46.26 40.995 47.604 40.995 49.26 c 40.995 50.916 39.651 52.26 37.995 52.26 c h 37.995 51.745 m 36.615 51.745 35.495 50.625 35.495 49.245 c 35.495 47.865 36.615 46.745 37.995 46.745 c 39.375 46.745 40.495 47.865 40.495 49.245 c 40.495 50.625 39.375 51.745 37.995 51.745 c h 38.01 51.245 m 36.906 51.245 36.01 50.349 36.01 49.245 c 36.01 48.141 36.906 47.245 38.01 47.245 c 39.114 47.245 40.01 48.141 40.01 49.245 c 40.01 50.349 39.114 51.245 38.01 51.245 c h 37.995 50.76 m 37.167 50.76 36.495 50.088 36.495 49.26 c 36.495 48.432 37.167 47.76 37.995 47.76 c 38.823 47.76 39.495 48.432 39.495 49.26 c 39.495 50.088 38.823 50.76 37.995 50.76 c h 37.995 50.245 m 37.443 50.245 36.995 49.797 36.995 49.245 c 36.995 48.693 37.443 48.245 37.995 48.245 c 38.547 48.245 38.995 48.693 38.995 49.245 c 38.995 49.797 38.547 50.245 37.995 50.245 c h 38.01 49.745 m 37.734 49.745 37.51 49.521 37.51 49.245 c 37.51 48.969 37.734 48.745 38.01 48.745 c 38.286 48.745 38.51 48.969 38.51 49.245 c 38.51 49.521 38.286 49.745 38.01 49.745 c s 574 49.25 m 574 57.26 l 569.578 57.26 565.99 53.672 565.99 49.25 c 565.99 44.828 569.578 41.24 574 41.24 c 578.422 41.24 582.01 44.828 582.01 49.25 c 582.01 53.672 578.422 57.26 574 57.26 c f 573.99 57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 65 0 obj > /ExtGState > >> endobj 67 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (235)Tj /F2 1 Tf 9 0 0 9 126 678.75 Tm [(We)-264.4(can)-263.9(solve)-264.4(this)-264.5(problem)-263.8(with)-264.1(more)-264.8(data:)-264.1(a)-263.3(list)-265.3(of)-263.4(misspellings.)-264.6(Roger)-263.5(Mitton)-265(has)-263.3(a)-264.5(list)-264.2(of)]TJ 0 -1.4444 TD [(about)-273(40,000)]TJ /F6 1 Tf 6.1411 0 TD (c,w)Tj /F2 1 Tf 1.58 0 TD [(pairs)-272.4(at)]TJ /F6 1 Tf 3.4911 0 TD (http://www.dcs.bbk.ac.uk/~ROGER/corpora.html)Tj /F2 1 Tf 19.8289 0 TD [(.)-273.1(But)-273.4(we)-272.8(cant)-272.9(hope)]TJ -31.0411 -1.4444 TD (to just look up P\()Tj /F6 1 Tf 7.67 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD (=thew |)Tj /F6 1 Tf 3.6367 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (=thaw\) from this data; with only 40,000 examples, chances)Tj -12.3633 -1.4444 TD (are slim that we will have seen this exact pair before. When data is sparse, we need to)Tj T* (generalize. We can do that by ignoring the letters that are the same, the th and w,)Tj T* [(leaving)-271.5(us)-271.1(with)-271.9(P\()]TJ /F6 1 Tf 8 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD [(=e)-272.2(|)]TJ /F6 1 Tf 1.8656 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD [(=a\),)-271.9(the)-271.5(probability)-271(that)-271.9(an)-271.2(e)-272(was)-270.4(typed)-271.3(when)-271.9(the)-271.5(correct)-271.6(letter)]TJ -10.9211 -1.4444 TD [(was)-274.9(a.)-274(This)-273.8(is)-275.2(one)-274.1(of)-274.5(the)-273.8(most)-275.1(common)-274.7(errors)-273.5(in)-274.3(the)-274.9(misspelling)-273.8(data,)-275.2(due)-274.1(to)-274.3(confusions)]TJ T* (like consistent/consistant and inseparable/inseperable.)Tj 0 -2.2222 TD (In the following table we consider five candidates for)Tj /F6 1 Tf 23.8189 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD ( when)Tj /F6 1 Tf 3.0922 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD (=thew. One is thew itself,)Tj -27.9678 -1.4444 TD (and the other four represent the four types of single edits that we will consider: \(1\) We)Tj T* (can)Tj /F6 1 Tf 1.8333 0 TD (delete)Tj /F2 1 Tf 2.2222 0 TD ( the letter w in thew, yielding the. \(2\) We can)Tj /F6 1 Tf 23.39 0 TD (insert)Tj /F2 1 Tf 2.2233 0 TD ( an r to get threw.)Tj -29.6689 -1.4444 TD (For both these edits, we condition on the previous letter. \(3\) We can replace e with a)Tj T* (as mentioned earlier. \(4\) We can transpose two adjacent letters, swapping ew with)Tj T* [(we.)-275.6(We)-276.7(say)-275.1(that)-276.3(these)-275.9(single)-276.2(edits)-275.1(are)-276.5(at)]TJ /F6 1 Tf 18.8344 0 TD [(edit)-248.3(distance)]TJ /F2 1 Tf 5.1378 0 TD [(1;)-276(a)-275.6(candidate)-276.4(that)-276.3(requires)-275.7(two)-276(sin-)]TJ -23.9722 -1.4444 TD (gle edits is at edit distance 2. The table shows the words)Tj /F6 1 Tf 25.0056 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( and)Tj /F6 1 Tf 2.2233 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (, the edit)Tj /F6 1 Tf 4.2222 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (, the proba-)Tj -34.3422 -1.4444 TD (bility P\()Tj /F6 1 Tf 3.4644 0 TD (w)Tj /F2 1 Tf 0.7211 0 TD ( |)Tj /F6 1 Tf 0.7789 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD (\), the probability P\()Tj /F6 1 Tf 8.6689 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\), and the product of the probabilities \(scaled for)Tj -14.3011 -1.4444 TD (readability\).)Tj 0 -12.6111 TD (We see from the table that the is the most likely correction. P\()Tj /F6 1 Tf 28.5011 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\) can be computed with)Tj /F8 1 Tf 8.1 0 0 8.1 126 337.25 Tm ( 7)Tj /F2 1 Tf 9 0 0 9 134.1 337.25 Tm (. For P\()Tj /F6 1 Tf 3.28 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\) we need to create a new function,)Tj /F8 1 Tf 8.1 0 0 8.1 325.14 337.25 Tm ( )Tj /F2 1 Tf 9 0 0 9 345.39 337.25 Tm (, which gives the probability of an)Tj -24.3767 -1.4444 TD (edit, estimated from the misspelling corpus. For example,)Tj /F8 1 Tf 8.1 0 0 8.1 357.87 324.25 Tm ( 147F43)Tj /F2 1 Tf 9 0 0 9 410.52 324.25 Tm ( is .000007. More)Tj -31.6133 -1.4444 TD (complicated edits are defined as a concatenation of single edits. For example, to get from)Tj T* (hallow to hello we concatenate)Tj /F8 1 Tf 8.1 0 0 8.1 269.67 298.25 Tm (F)Tj /F2 1 Tf 9 0 0 9 281.82 298.25 Tm ( with)Tj /F8 1 Tf 8.1 0 0 8.1 305.15 298.25 Tm (7F)Tj /F2 1 Tf 9 0 0 9 321.35 298.25 Tm (, so the whole edit is called)Tj /F8 1 Tf 8.1 0 0 8.1 431.72 298.25 Tm (F=7F)Tj /F2 1 Tf 9 0 0 9 464.12 298.25 Tm ( \(or)Tj /F8 1 Tf 8.1 0 0 8.1 126 285.25 Tm (7F=F)Tj /F2 1 Tf 9 0 0 9 158.4 285.25 Tm [(,)-253.1(which)-253.2(in)-254.3(this)-253.4(casebut)-252.6(not)-253.3(alwaysis)-254(the)-253.8(same)-253(thing\).)-253.3(The)-253(probability)-254.3(of)-253.4(a)-253.3(com-)]TJ -3.6 -1.4444 TD (plex edit is taken to be the product of its components.)Tj 0 -2.2222 TD (A problem: what the probability of the empty edit,)Tj /F8 1 Tf 8.1 0 0 8.1 330.86 252.25 Tm ( 1443)Tj /F2 1 Tf 9 0 0 9 367.31 252.25 Tm (? That is, given that the)Tj -26.8122 -1.4444 TD (intended word is)Tj /F6 1 Tf 7.7622 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD (, how likely is it that the author would actually type)Tj /F6 1 Tf 23.4678 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD (, rather than one)Tj -31.8967 -1.4444 TD (of the possible edits that yields an error? That depends on the skill of the typist and on)Tj T* (whether any proofreading has been done. Rather arbitrarily, I assumed that a spelling)Tj T* [(error)-267(occurs)-268.1(once)-266.8(every)-267(20)-268(words.)-267(Note)-267.9(that)-267.4(if)-267(I)-266.9(had)-267.4(assumed)-267(errors)-268(occur)-267.1(only)-266.9(once)-267.9(in)-266.5(50)]TJ T* (words, then P\()Tj /F6 1 Tf 6.5389 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\) for)Tj /F6 1 Tf 2.2044 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD (="thew would be .98, not .95, and thew would become the)Tj -11.3 -1.4444 TD (most probable answer.)Tj 0 -2.2222 TD (Finally, were ready to show the code. There are two top-level functions,)Tj /F8 1 Tf 8.1 0 0 8.1 419.9 154.25 Tm ()Tj /F2 1 Tf 9 0 0 9 448.25 154.25 Tm (, which)Tj -35.8056 -1.4444 TD (returns the best correction for a single word, and)Tj /F8 1 Tf 8.1 0 0 8.1 324.04 141.25 Tm ()Tj /F2 1 Tf 9 0 0 9 368.59 141.25 Tm (, which applies)Tj /F8 1 Tf 8.1 0 0 8.1 430.94 141.25 Tm ()Tj /F2 1 Tf 9 0 0 9 459.29 141.25 Tm ( to)Tj /F15 1 Tf 8 0 0 8 132 439.22 Tm 6.061 Tc [(wc)-265(w)]TJ /F1 1 Tf 14.1887 0 TD 0 Tc ( |)Tj /F15 1 Tf 0.6725 0 TD (c)Tj /F1 1 Tf 5.3888 0 TD (P\()Tj /F15 1 Tf 0.8025 0 TD (w)Tj /F1 1 Tf 0.6887 0 TD ( |)Tj /F15 1 Tf 0.6725 0 TD (c)Tj /F1 1 Tf 0.4238 0 TD 3.8675 Tc [(\)P)3867.5(\()]TJ /F15 1 Tf 4.965 0 TD 0 Tc (c)Tj /F1 1 Tf 0.425 0 TD 5.2275 Tc [(\)1)5227.5(0)]TJ 6 0 0 6 410.13 441.32 Tm 0 Tc (9)Tj 8 0 0 8 413.17 439.22 Tm ( P\()Tj /F15 1 Tf 0.9825 0 TD (w)Tj /F1 1 Tf 0.6888 0 TD ( |)Tj /F15 1 Tf 0.6725 0 TD (c)Tj /F1 1 Tf 0.4238 0 TD (\) P\()Tj /F15 1 Tf 1.2775 0 TD (c)Tj /F1 1 Tf 0.4238 0 TD (\))Tj /F3 1 Tf -39.615 -1.625 TD [(thew)-4889(the)-5544(ew | e)-4541(.000007)-3821(.02)-5653(144.)]TJ T* [(thew)-4889(thew)-11639(.95)-5644(.00000009)-2905( 90.)]TJ T* [(thew)-4889(thaw)-4901(e | a)-5208(.001)-5195(.0000007)-3363( 0.7)]TJ T* [(thew)-4889(threw)-4562(h | hr)-4793(.000008)-3821(.000004)-3821( 0.03)]TJ T* [(thew)-4889(thwe)-4889(ew | we)-3886(.000003)-3821(.00000004)-2905( 0.0001)]TJ ET 0 G 0 J 0 j 0.51 w 3.86 M []0 d 126 370.8 m 126 448.3 l B* 180 370.3 m 180 448.8 l B* 234 370.3 m 234 448.8 l B* 288 370.3 m 288 448.8 l B* 342 370.3 m 342 448.8 l B* 396 370.3 m 396 448.8 l B* 486 370.8 m 486 448.3 l B* 486.25 448.55 m 125.75 448.55 l B* 486.25 435.55 m 125.75 435.55 l B* 486.25 422.55 m 125.75 422.55 l B* 486.25 409.55 m 125.75 409.55 l B* 486.25 396.55 m 125.75 396.55 l B* 486.25 383.55 m 125.75 383.55 l B* q 9 771.75 594 -751.5 re W n 486.25 370.55 m 125.75 370.55 l B* 1 G 0.75 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 235 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0.27 w 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 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744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 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742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 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50.349 36.01 49.245 c 36.01 48.141 36.906 47.245 38.01 47.245 c 39.114 47.245 40.01 48.141 40.01 49.245 c 40.01 50.349 39.114 51.245 38.01 51.245 c h 37.995 50.76 m 37.167 50.76 36.495 50.088 36.495 49.26 c 36.495 48.432 37.167 47.76 37.995 47.76 c 38.823 47.76 39.495 48.432 39.495 49.26 c 39.495 50.088 38.823 50.76 37.995 50.76 c h 37.995 50.245 m 37.443 50.245 36.995 49.797 36.995 49.245 c 36.995 48.693 37.443 48.245 37.995 48.245 c 38.547 48.245 38.995 48.693 38.995 49.245 c 38.995 49.797 38.547 50.245 37.995 50.245 c h 38.01 49.745 m 37.734 49.745 37.51 49.521 37.51 49.245 c 37.51 48.969 37.734 48.745 38.01 48.745 c 38.286 48.745 38.51 48.969 38.51 49.245 c 38.51 49.521 38.286 49.745 38.01 49.745 c s 574 49.25 m 574 57.26 l 569.578 57.26 565.99 53.672 565.99 49.25 c 565.99 44.828 569.578 41.24 574 41.24 c 578.422 41.24 582.01 44.828 582.01 49.25 c 582.01 53.672 578.422 57.26 574 57.26 c f 573.99 57.245 m 569.574 57.245 565.99 53.661 565.99 49.245 c 565.99 44.829 569.574 41.245 573.99 41.245 c 578.406 41.245 581.99 44.829 581.99 49.245 c 581.99 53.661 578.406 57.245 573.99 57.245 c s 0 g 574 49.25 m 574.349 57.252 l 574.233 57.257 574.116 57.26 574 57.26 c f 574 49.25 m 575.734 57.07 l 575.62 57.095 575.506 57.118 575.391 57.138 c f 574 49.25 m 577.065 56.65 l 576.958 56.695 576.849 56.737 576.74 56.777 c f 574 49.25 m 578.304 56.006 l 578.205 56.068 578.106 56.129 578.005 56.187 c f 574 49.25 m 579.411 55.156 l 579.326 55.234 579.238 55.311 579.149 55.386 c f 574 49.25 m 580.355 54.126 l 580.284 54.219 580.211 54.309 580.136 54.399 c f 574 49.25 m 581.105 52.949 l 581.051 53.052 580.995 53.154 580.937 53.255 c f 574 49.25 m 581.639 51.659 l 581.604 51.77 581.567 51.88 581.527 51.99 c f 574 49.25 m 581.941 50.296 l 581.926 50.411 581.909 50.526 581.888 50.641 c f 574 49.25 m 582.002 48.901 l 582.007 49.017 582.01 49.133 582.01 49.25 c f 574 49.25 m 581.82 47.516 l 581.845 47.63 581.868 47.744 581.888 47.859 c f 574 49.25 m 581.4 46.185 l 581.445 46.292 581.487 46.401 581.527 46.51 c f 574 49.25 m 580.755 44.946 l 580.818 45.044 580.879 45.144 580.937 45.245 c f 574 49.25 m 579.906 43.839 l 579.984 43.924 580.061 44.012 580.136 44.101 c f 574 49.25 m 578.876 42.895 l 578.969 42.966 579.059 43.039 579.149 43.114 c f 574 49.25 m 577.699 42.145 l 577.802 42.199 577.904 42.255 578.005 42.313 c f 574 49.25 m 576.409 41.611 l 576.52 41.646 576.63 41.683 576.74 41.723 c f 574 49.25 m 575.046 41.309 l 575.161 41.324 575.276 41.341 575.391 41.362 c f 574 49.25 m 573.651 41.248 l 573.767 41.243 573.883 41.24 574 41.24 c f 574 49.25 m 572.266 41.43 l 572.38 41.405 572.494 41.382 572.609 41.362 c f 574 49.25 m 570.935 41.85 l 571.042 41.805 571.151 41.763 571.26 41.723 c f 574 49.25 m 569.696 42.494 l 569.794 42.432 569.894 42.371 569.995 42.313 c f 574 49.25 m 568.589 43.344 l 568.674 43.266 568.762 43.189 568.851 43.114 c f 574 49.25 m 567.645 44.374 l 567.716 44.281 567.789 44.191 567.864 44.101 c f 574 49.25 m 566.895 45.551 l 566.949 45.448 567.005 45.346 567.063 45.245 c f 574 49.25 m 566.361 46.841 l 566.396 46.73 566.433 46.62 566.473 46.51 c f 574 49.25 m 566.058 48.204 l 566.074 48.089 566.091 47.974 566.112 47.859 c f 574 49.25 m 565.998 49.599 l 565.993 49.483 565.99 49.367 565.99 49.25 c f 574 49.25 m 566.18 50.984 l 566.155 50.87 566.132 50.756 566.112 50.641 c f 574 49.25 m 566.6 52.315 l 566.555 52.208 566.513 52.099 566.473 51.99 c f 574 49.25 m 567.244 53.554 l 567.182 53.456 567.121 53.356 567.063 53.255 c f 574 49.25 m 568.094 54.661 l 568.016 54.576 567.939 54.488 567.864 54.399 c f 574 49.25 m 569.124 55.605 l 569.031 55.534 568.94 55.461 568.851 55.386 c f 574 49.25 m 570.301 56.355 l 570.198 56.301 570.096 56.245 569.995 56.187 c f 574 49.25 m 571.591 56.889 l 571.48 56.854 571.37 56.817 571.26 56.777 c f 574 49.25 m 572.954 57.191 l 572.839 57.176 572.724 57.159 572.609 57.138 c f endstream endobj 68 0 obj > /ExtGState > >> endobj 70 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (236)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 126 678.75 Tm 0 Tc (every word in a text, leaving the surrounding characters intact. The candidates are all the)Tj 0 -1.4444 TD (possible edits, and the best is the one with the highest P\()Tj /F6 1 Tf 25.1711 0 TD (w)Tj /F2 1 Tf 0.7222 0 TD ( |)Tj /F6 1 Tf 0.7778 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\) P\()Tj /F6 1 Tf 1.6111 0 TD (c)Tj /F2 1 Tf 0.3344 0 TD (\) score:)Tj /F8 1 Tf 8 0 0 8 138 646.42 Tm ()Tj /F13 1 Tf 2 0 TD (\015\015 )Tj /F8 1 Tf 5.5 0 TD (103:)Tj -7.5 -1.25 TD ( ;-$G 7 0 %145GE\015GM6=42 \012% \012: 1\012$1332 03)Tj 0 -2.5 TD ()Tj /F13 1 Tf 2 0 TD (\015\015)Tj /F8 1 Tf 3.5 0 TD (173:)Tj -5.5 -1.25 TD ( ;# 7 \012 ! $ 7 / 173\0121)-166.5(3)]TJ T* ( 2 / \012012 !/\012% 123: 13 C 7133)Tj T* ( )Tj /F2 1 Tf 9 0 0 9 126 548.75 Tm (P\()Tj /F6 1 Tf 0.9456 0 TD (w)Tj /F2 1 Tf 0.7211 0 TD ( |)Tj /F6 1 Tf 0.7789 0 TD (c)Tj /F2 1 Tf 0.3333 0 TD (\) is computed by)Tj /F8 1 Tf 8.1 0 0 8.1 220.18 548.75 Tm ( )Tj /F2 1 Tf 9 0 0 9 240.43 548.75 Tm (:)Tj /F8 1 Tf 8 0 0 8 138 529.42 Tm ()Tj /F13 1 Tf 2 0 TD (\012 )Tj /F8 1 Tf 2.5 0 TD (13:)Tj -4.5 -1.25 TD ( ;& $%% W % 44 4F%4 4F%=F4 // 44: 1"$@3)Tj T* ( $@$@C$1 "13 $14=433)Tj /F13 1 Tf 0 -2.5 TD (\015\015\015)Tj /F8 1 Tf 6.5 0 TD ( / "<.> )Tj /F8 1 Tf 3 0 TD ( / 114"433 DD %% )Tj /F2 1 Tf 9 0 0 9 126 441.75 Tm [(The)-239.7(candidates)-239.6(are)-239.9(generated)-239.8(by)]TJ /F8 1 Tf 8.1 0 0 8.1 255.47 441.75 Tm ()Tj /F2 1 Tf 9 0 0 9 275.72 441.75 Tm [(,)-239.8(which)-239.9(is)-239.7(passed)-240(a)-240(word,)-239.3(and)-240.8(returns)-239.1(a)-240(dict)-240.1(of)-240.1({word:)]TJ -16.6356 -1.4444 TD (edit} pairs indicating the possible corrections. In general there will be several edits that)Tj T* [(arrive)-253.6(at)-252.6(a)-253.3(correction.)-253.1(\(For)-253.3(example,)-252.8(we)-253.9(can)-252.8(get)-252.5(from)-253.1(tel)-253.2(to)-253.2(tell)-253(by)-253.8(inserting)-253.2(an)-253.4(l)-252.9(after)]TJ T* [(the)-274.9(e)-275.3(or)-276.1(after)-275.2(the)-274.9(l.\))-274.8(We)-275.5(choose)-275.1(the)-276(edit)-275.2(with)-275.2(the)-274.9(highest)-275.7(probability.)]TJ /F8 1 Tf 8.1 0 0 8.1 417.35 402.75 Tm ()Tj /F2 1 Tf 9 0 0 9 440.07 402.75 Tm [(is)-275.2(the)-276(most)]TJ -34.8967 -1.4444 TD (complex function weve seen so far. In part this is inherent; it)Tj /F6 1 Tf 27.6511 0 TD (is)Tj /F2 1 Tf 0.6122 0 TD ( complicated to generate)Tj -28.2633 -1.4444 TD [(four)-236.8(kinds)-237.8(of)-236.8(edits.)-237.1(But)-236.8(in)-237.7(part)-236.4(it)-237.9(is)-236.3(because)-237.9(we)-236.1(took)-237.9(some)-237(efforts)-237.4(to)-236.5(make)]TJ /F8 1 Tf 8.1 0 0 8.1 414.68 376.75 Tm ()Tj /F2 1 Tf 9 0 0 9 437.07 376.75 Tm [(efficient.)-236.9(\(A)]TJ -34.5633 -1.4444 TD (slower but easier-to-read version is at)Tj /F6 1 Tf 17.0044 0 TD (http://norvig.com/spell-correct.html)Tj /F2 1 Tf 14.0333 0 TD (.\) If we considered)Tj /F6 1 Tf -31.0378 -1.4444 TD (all)Tj /F2 1 Tf 1.0556 0 TD ( edits, a word like acommodations would yield 233,166 candidates. But only 11 of)Tj -1.0556 -1.4444 TD (these are in the vocabulary. So)Tj /F8 1 Tf 8.1 0 0 8.1 252.02 337.75 Tm ()Tj /F2 1 Tf 9 0 0 9 272.27 337.75 Tm ( works by precomputing the set of all prefixes of all)Tj -16.2522 -1.4444 TD [(the)-259.3(words)-259.4(in)-259.9(the)-259.3(vocabulary.)-259.6(It)-259.4(then)-259.4(calls)]TJ /F8 1 Tf 8.1 0 0 8.1 291 324.75 Tm (#)Tj /F2 1 Tf 9 0 0 9 317.64 324.75 Tm [(recursively,)-258.8(splitting)-259.5(the)-259.3(word)-259.5(into)-259.8(a)-258.9(head)]TJ -21.2933 -1.4444 TD [(and)-245.2(a)-246.7(tail)-245.4(\()]TJ /F8 1 Tf 8.1 0 0 8.1 168.14 311.75 Tm ()Tj /F2 1 Tf 9 0 0 9 178.45 311.75 Tm (and)Tj /F8 1 Tf 8.1 0 0 8.1 195.66 311.75 Tm ()Tj /F2 1 Tf 9 0 0 9 205.97 311.75 Tm [(in)-246.6(the)-244.9(code\))-246.1(and)-245.2(assuring)-246.3(that)-245.2(the)-246(head)-245.2(is)-246.3(always)-245.4(in)-245.4(the)-246(list)-245.3(of)-245.7(prefixes.)]TJ -8.8856 -1.4444 TD (The results are collected by adding to the dict)Tj /F8 1 Tf 8.1 0 0 8.1 309.2 298.75 Tm ()Tj /F2 1 Tf 9 0 0 9 337.55 298.75 Tm (:)Tj /F8 1 Tf 8 0 0 8 138 279.42 Tm ()Tj /F13 1 Tf 2 0 TD ( )Tj /F8 1 Tf 2.5 0 TD (172 /3:)Tj -4.5 -1.25 TD ( ;# Y: Z $ 7 7 / YZ)Tj T* ( )Tj /F13 1 Tf 4 0 TD ( )Tj /F8 1 Tf 3 0 TD (12 2 2 3:)Tj -7 -1.25 TD ( )Tj /F13 1 Tf 6 0 TD ()Tj /F8 1 Tf 1 0 TD (1>2#3: =5#=4F4=>6)Tj -7 -1.25 TD ( / =)Tj T* ( 7:)Tj T* ( / 4=413)Tj T* ( : 56 / )Tj T* ( : 56 / \01201562 2 !/ 3)Tj T* ( \(/ : )Tj T* ( 0 / 5= $% = #BLUB-6)Tj T* ( $ / 15G"6 4\(43 DD $8 )Tj T* ( DD )Tj T* ( 0:)Tj T* ( #12 2 G"2 1$=5G"62 $33)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 236 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 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#BLUB-:)Tj T* ( #1=5"62 56=5:62 G"2)Tj T* ( 15"6=562 5:633)Tj T* ( DD ? :)Tj T* ( #1442 72 2 563)Tj T* ( )Tj /F13 1 Tf 0 -2.5 TD (\012 !)Tj /F8 1 Tf 4 0 TD ( / 175:6 7 7 1173 = "33)Tj /F2 1 Tf 9 0 0 9 126 501.75 Tm (Heres an example of)Tj /F8 1 Tf 8.1 0 0 8.1 212.85 501.75 Tm ()Tj /F2 1 Tf 9 0 0 9 233.1 501.75 Tm (:)Tj /F8 1 Tf 8 0 0 8 138 482.42 Tm (,,, 14%42 3)Tj 0 -1.25 TD (Y4%4: 442 4%4: 4\(F\(=F42 4%4: 4\(F\(4Z)Tj /F2 1 Tf 9 0 0 9 126 454.75 Tm (And here is the spell corrector at work:)Tj /F8 1 Tf 8 0 0 8 138 435.42 Tm (,,, 148!%43)Tj T* (48%4)Tj 0 -2.5 TD (,,, 14\012%%43)Tj 0 -1.25 TD (4\012%%4)Tj 0 -2.5 TD (,,, 14 \012\012 !)Tj 0 -1.25 TD ( \012$ $ 7 \012\012 \012$)Tj T* ( $ 7$ )Tj 0 -1.25 TD (\012$ ")Tj T* (\012$ "")Tj T* (\012$ ')Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 237 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c h 573.99 743.255 m 573.714 743.255 573.49 743.031 573.49 742.755 c 573.49 742.479 573.714 742.255 573.99 742.255 c 574.266 742.255 574.49 742.479 574.49 742.755 c 574.49 743.031 574.266 743.255 573.99 743.255 c s 38 49.25 m 38 57.26 l 33.578 57.26 29.99 53.672 29.99 49.25 c 29.99 44.828 33.578 41.24 38 41.24 c 42.422 41.24 46.01 44.828 46.01 49.25 c 46.01 53.672 42.422 57.26 38 57.26 c f 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 38.01 57.245 m 33.594 57.245 30.01 53.661 30.01 49.245 c 30.01 44.829 33.594 41.245 38.01 41.245 c 42.426 41.245 46.01 44.829 46.01 49.245 c 46.01 53.661 42.426 57.245 38.01 57.245 c h 37.995 56.76 m 33.855 56.76 30.495 53.4 30.495 49.26 c 30.495 45.12 33.855 41.76 37.995 41.76 c 42.135 41.76 45.495 45.12 45.495 49.26 c 45.495 53.4 42.135 56.76 37.995 56.76 c h 37.995 56.245 m 34.131 56.245 30.995 53.109 30.995 49.245 c 30.995 45.381 34.131 42.245 37.995 42.245 c 41.859 42.245 44.995 45.381 44.995 49.245 c 44.995 53.109 41.859 56.245 37.995 56.245 c h 38.01 55.745 m 34.422 55.745 31.51 52.833 31.51 49.245 c 31.51 45.657 34.422 42.745 38.01 42.745 c 41.598 42.745 44.51 45.657 44.51 49.245 c 44.51 52.833 41.598 55.745 38.01 55.745 c h 37.995 55.26 m 34.683 55.26 31.995 52.572 31.995 49.26 c 31.995 45.948 34.683 43.26 37.995 43.26 c 41.307 43.26 43.995 45.948 43.995 49.26 c 43.995 52.572 41.307 55.26 37.995 55.26 c h 37.995 54.745 m 34.959 54.745 32.495 52.281 32.495 49.245 c 32.495 46.209 34.959 43.745 37.995 43.745 c 41.031 43.745 43.495 46.209 43.495 49.245 c 43.495 52.281 41.031 54.745 37.995 54.745 c h 38.01 54.245 m 35.25 54.245 33.01 52.005 33.01 49.245 c 33.01 46.485 35.25 44.245 38.01 44.245 c 40.77 44.245 43.01 46.485 43.01 49.245 c 43.01 52.005 40.77 54.245 38.01 54.245 c h 37.995 53.76 m 35.511 53.76 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TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 126 678.75 Tm 0 Tc [(The)-241.9(corpus)-242.8(uses)-242.1(the)-242.7(wrong)-242.3(word)-242.9(7%)-242.9(of)-242.3(the)-242.7(time.)-241.9(I)-242.4(can)-242.8(think)-242.1(of)-242.3(three)-242.5(ways)-242.3(to)-242.1(fix)-243.2(this.)-242.1(First,)]TJ 0 -1.4444 TD (we could acquire a list of dictionary words and only make a correction to a word in the)Tj T* [(dictionary.)-255.5(But)-255.7(a)-255.6(dictionary)-254.6(does)-255.7(not)-255.5(list)-255.3(all)-255.1(the)-256(newly)-255.6(coined)-255(words)-255(and)-256.3(proper)-255.1(names.)-255.1(\(A)]TJ T* (compromise might be to force lowercase words into the dictionary vocabulary, but allow)Tj T* (capitalized words that are not in the dictionary.\) Second, we could acquire a corpus that)Tj T* (has been carefully proofread, perhaps one restricted to books and periodicals from high-)Tj T* 0.01 Tc (quality publishers. Third, we could spell-correct the corpus we have. It may seem like)Tj T* [(circular)-275.9(reasoning)-276(to)-275.4(require)-275.9(spell-correction)-276.6(of)-275.7(the)-276(corpus)-276.1(before)-275.2(we)-276.1(can)-276.1(use)-275.5(it)-276.8(for)-275.6(spell-)]TJ T* -0.0156 Tc [(correction,)-234.2(but)-229(i)0(t)-229(c)0(an)-229.5(be)-228.6(done.)-230.1(For)-230.1(this)-229(application)-234.5(we)-228.4(would)-230.7(start)-230.5(by)-228.3(grouping)-232.3(t)0(ogether)-232.5(words)]TJ T* 0.0001 Tw (that are a small edit distance from each other. For each pair of close words, we would then)Tj T* (check to see if one is much more common than the other. If it is, we would then check the)Tj T* (bigram \(or trigram\) counts to see if the two words had similar distributions of neighboring)Tj T* 0 Tw (words. For example, here are four bigram counts for mispellings and misspellings:)Tj /F8 1 Tf 8 0 0 8 138 503.42 Tm 0 Tc (\012$ 7 '' \012$ 7 ")Tj 0 -1.25 TD (\012$ \012$ ')Tj T* (\012$ " \012$ "")Tj T* (\012$ \012$ "')Tj /F2 1 Tf 9 0 0 9 126 457.75 Tm (The two words share many bigram neighbors, always with misspellings being more)Tj 0 -1.4444 TD (common, so that is good evidence that mispellings is a misspelling. Preliminary tests)Tj T* -0.01 Tc (show that this approach works wellbut there is a problem: it would require hundreds of)Tj T* [(CPU)-256.1(hours)-255.1(of)-255.7(computation.)-255.9(It)-255(is)-255.2(appropriate)-255.8(for)-255.5(a)-255.6(cluster)-256(of)-255.7(machines,)-255.4(not)-255.5(a)-255.6(single)-255.1(computer.)]TJ 0 -2 TD 0 Tc (How does the data-driven approach compare to a more traditional software development)Tj 0 -1.4444 TD (process wherein the programmer codes explicit rules? To address that, well peek at the)Tj T* -0.01 Tc (spelling correction code from the ht://Dig project, an excellent open source intranet search)Tj T* (engine. Given a word, ht://Digs)Tj /F8 1 Tf 8.1 0 0 8.1 254.23 361.75 Tm (\012$)Tj /F2 1 Tf 9 0 0 9 289.95 361.75 Tm ( routine produces a)Tj /F6 1 Tf 8.6911 0 TD (key)Tj /F2 1 Tf 1.3022 0 TD ( representing the sound of)Tj -28.21 -1.4444 TD (the word. For example, both tough and tuff map to the key TF, and thus would be)Tj T* [(candidates)-251.8(for)-252.2(misspellings)-252.6(of)-252.3(each)-251.7(other.)-251.9(Here)-252.3(is)-253(part)-252(of)-252.3(the)]TJ /F8 1 Tf 8.1 0 0 8.1 359.81 335.75 Tm (\012$)Tj /F2 1 Tf 9 0 0 9 397.8 335.75 Tm [(code)-251.8(for)-252.2(the)-252.7(letter)-252.5(G:)]TJ /F8 1 Tf 8 0 0 8 138 318.42 Tm 0 Tc ( 4O4:)Tj 0 -1.25 TD ( .C)Tj T* ( C L GOK ?GGOK2 NGGOK2)Tj T* ( C GKGGOK2 GKGGGOK $$ )Tj T* ( C GO*BN2 GO*2 GNOBG2 GNOG2 GNOJG)Tj T* ( C P GOBG2 GOG2 GOJG )Tj T* ( C OO +)Tj T* ( C.)Tj T* ( 11C1 = "3 [/ 4O4 FF 871C1 = 333 \\\\)Tj T* ( 1C1 = "3 [/ 4*4 FF 1C1 = "3 \\\\)Tj T* ( 1C1 = 3 [/ 4B4 FF)Tj T* ( C1 = 3 [/ 4N4333 \\\\)Tj T* ( 1C1 G "3 [/ 4N4 FF [81C1 = "3333)Tj T* ( 181C1 = "33 \\\\ C1 = 3 [/ 4O43)Tj T* ( ! \(\( 4P4W)Tj T* ( )Tj T* ( ! \(\( 4+4W)Tj T* ( 1C1 = "3 // 4K4 \\\\ [1C1 G 33 \\\\)Tj T* ( C1 G 3 [/ 4K43)Tj T* ( ! \(\( 4L4W)Tj T* ( %!W)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M 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endstream endobj 77 0 obj > /ExtGState > >> endobj 79 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F3 1 Tf 7.5 0 0 7.5 354.6 96.43 Tm 0 g 0.2 Tc 0 Tw (NATURAL LANGUAGE CORPUS DATA)Tj /F1 1 Tf 20.796 0 TD 0 Tc (239)Tj /F2 1 Tf 9 0 0 9 126 678.75 Tm (This code correctly maps GH to F in TOUGH and not in BOUGH. But have the)Tj 0 -1.4444 TD (rules correctly captured all the cases? What about OUGHT? Or COUGH versus HIC-)Tj T* (COUGH? We can write test cases to verify each branch of the code, but even then we)Tj T* [(wont)-240.3(know)-240.9(what)-239.9(words)-240.5(were)]TJ /F6 1 Tf 13.5011 0 TD (not)Tj /F2 1 Tf 1.5178 0 TD [(covered.)-240(What)-240.4(happens)-240.3(when)-240.8(a)-240(new)-240.7(word)-240.6(like)-240.2(iPhone)]TJ -15.0189 -1.4444 TD [(is)-237.4(introduced?)-238.2(Clearly,)-237.4(the)-238.2(handwritten)-237.4(rules)-237.4(are)-238.8(difficult)-237.5(to)-237.7(develop)-238.1(and)-237.4(maintain.)-237.4(The)-237.4(big)]TJ T* (advantage of the data-driven method is that so much knowledge is encoded in the data,)Tj T* (and new knowledge can be added just by collecting more data. But another advantage is)Tj T* (that, while the data can be massive, the code is succinctabout 50 lines for)Tj /F8 1 Tf 8.1 0 0 8.1 430.19 587.75 Tm ()Tj /F2 1 Tf 9 0 0 9 458.54 587.75 Tm (, com-)Tj -36.9489 -1.4444 TD (pared to over 1,500 for ht://Digs spelling code. As the great ex-programmer Bill Gates)Tj T* (once said, Measuring programming progress by lines of code is like measuring aircraft)Tj T* (building progress by weight. Gates knew that lines of code are more a liability than an)Tj T* (asset. The probabilistic data-driven methodology is the ultimate in agile programming.)Tj 0 -2.2222 TD (Another issue is portability. If we wanted a Latvian spelling-corrector, the English)Tj /F8 1 Tf 8.1 0 0 8.1 126 502.75 Tm (\012$)Tj /F2 1 Tf 9 0 0 9 164.77 502.75 Tm [(rules)-258.5(would)-257.3(be)-258.6(of)-257.9(little)-257.8(use.)-258.7(To)-256.9(port)-258.2(the)-258.2(data-driven)]TJ /F8 1 Tf 8.1 0 0 8.1 369.86 502.75 Tm ()Tj /F2 1 Tf 9 0 0 9 400.54 502.75 Tm [(algorithm)-258.1(to)-257.7(another)]TJ -30.5044 -1.4444 TD (language, all we need is a large corpus of Latvian; the code remains unchanged.)Tj /F1 1 Tf 15 0 0 15 126 460.75 Tm [(Other T)72(asks)]TJ /F2 1 Tf 9 0 0 9 126 441.75 Tm (Here are some more tasks that have been handled with probabilistic language models.)Tj /F1 1 Tf 12.5 0 0 12.5 126 417.42 Tm (Language Identification)Tj /F2 1 Tf 9 0 0 9 126 399.75 Tm (There are web protocols for declaring what human language a page is written in. In fact)Tj T* (there are at least two protocols, one in HTML and one in HTTP, but sometimes the proto-)Tj T* (cols disagree, and sometimes they both lie, so search engines usually classify pages based)Tj T* [(on)-240.8(the)-240.4(actual)-240.6(content,)-240.6(after)-240.8(collecting)-241.3(some)-240.3(samples)-241.1(for)-240(each)-241.7(known)-239.9(language.)-240.8(Your)-240.8(task)-240.9(is)]TJ T* (to write such a classifier. State of the art is over 99% accuracy.)Tj /F1 1 Tf 12.5 0 0 12.5 126 323.42 Tm [(Spam Detection and Other Classification T)72.4(asks)]TJ /F2 1 Tf 9 0 0 9 126 305.75 Tm [(It)-250.6(is)-249.7(estimated)-249.6(that)-249.7(100)-250.9(billion)-249.5(spam)-250.3(email)-249.3(messages)-250.5(are)-249.9(sent)-250.3(every)-249.2(day.)-250.1(Given)-249.8(two)-250.4(corpora)]TJ T* [(of)-257.9(spam)-258.1(and)-257.4(nonspam)-259(messages,)-258.1(your)-257(task)-258.7(is)-257.4(to)-258.8(classify)-257.8(incoming)-257.3(messages.)-258.1(The)-258.5(best)-257.7(spam)]TJ T* [(classifiers)-244.3(have)-244.2(models)-244.1(for)-244.4(word)]TJ /F6 1 Tf 14.2622 0 TD (n)Tj /F2 1 Tf 0.5556 0 TD [(-grams)-245(\(a)-244.3(message)-244(with)-244.1(10,000,000.00)-244.2(will)-244.3(be)-245.2(released)]TJ -14.8178 -1.4444 TD (and our country Nigeria is probably spam\) and character)Tj /F6 1 Tf 26.3167 0 TD (n)Tj /F2 1 Tf 0.5567 0 TD (-grams \(v1agra is probably)Tj -26.8733 -1.4444 TD (spam\), among other features. State of the art on this task is also over 99%, which keeps)Tj T* (the spam blockers slightly ahead of the spammers. Once you can classify documents as)Tj T* -0.01 Tc [(spam/nonspam,)-227.8(it)-226.8(is)-227.4(a)-226.7(short)-227.5(step)-227.5(to)-226.6(do)-228(other)-226.5(types)-227.2(of)-227.9(classification,)-226.7(such)-227.2(as)-227.7(urgent/nonurgent)]TJ T* 0.0056 Tc (email messages, or politics/business/sports/etc. for news articles, or favorable/neutral/)Tj T* 0.002 Tc -0.002 Tw [(unfavorable)-280.6(for product reviews.)]TJ /F1 1 Tf 12.5 0 0 12.5 126 177.42 Tm 0 Tc 0 Tw [(Author Identification \(Stylometr)-37(y\))]TJ /F2 1 Tf 9 0 0 9 126 159.75 Tm (Language models have been used to try to identify the disputed authors of the Federalist)Tj T* (Papers, Shakespeares poems, and Biblical verses. Similar techniques are used in tracking)Tj T* (terrorist groups and in criminal law, to identify and link perpetrators. This field is less)Tj T* [(mature;)-266.5(we)-267.2(dont)-267.1(yet)-266.7(know)-267.5(for)-266.7(sure)-266.5(what)-267.6(the)-266(best)-267.7(practices)-267(are,)-266.3(nor)-267.3(what)-266.5(accuracy)-267.6(rate)-266.9(to)]TJ ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 239 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c f 0 G 0 J 0 j 0.27 w 3.86 M []0 d 36 402 m 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c s 45 396 m 18 396 l B* 36 372 m 36 420 l B* 0 g 36 396 m 36 399 l 34.344 399 33 397.656 33 396 c 33 394.344 34.344 393 36 393 c 37.656 393 39 394.344 39 396 c 39 397.656 37.656 399 36 399 c f 1 G 0.33 w 39 396 m 33 396 l B* 36 393 m 36 399 l B* 1 g 576 396 m 576 402 l 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c f 0 G 0.27 w 576 402 m 572.688 402 570 399.312 570 396 c 570 392.688 572.688 390 576 390 c 579.312 390 582 392.688 582 396 c 582 399.312 579.312 402 576 402 c s 594 396 m 567 396 l B* 576 372 m 576 420 l B* 0 g 576 396 m 576 399 l 574.344 399 573 397.656 573 396 c 573 394.344 574.344 393 576 393 c 577.656 393 579 394.344 579 396 c 579 397.656 577.656 399 576 399 c f 1 G 0.33 w 579 396 m 573 396 l B* 576 393 m 576 399 l B* 1 g 306 47.25 m 306 53.25 l 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c f 0 G 0.27 w 306 53.25 m 302.688 53.25 300 50.562 300 47.25 c 300 43.938 302.688 41.25 306 41.25 c 309.312 41.25 312 43.938 312 47.25 c 312 50.562 309.312 53.25 306 53.25 c s 330 47.25 m 282 47.25 l B* 306 29.25 m 306 56.25 l B* 0 g 306 47.25 m 306 50.25 l 304.344 50.25 303 48.906 303 47.25 c 303 45.594 304.344 44.25 306 44.25 c 307.656 44.25 309 45.594 309 47.25 c 309 48.906 307.656 50.25 306 50.25 c f 1 G 0.33 w 309 47.25 m 303 47.25 l B* 306 44.25 m 306 50.25 l B* 1 g 66 744.75 m 66 750.75 l 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c f 0 G 0.27 w 66 750.75 m 62.688 750.75 60 748.062 60 744.75 c 60 741.438 62.688 738.75 66 738.75 c 69.312 738.75 72 741.438 72 744.75 c 72 748.062 69.312 750.75 66 750.75 c s 90 744.75 m 57 744.75 l B* 66 735.75 m 66 762.75 l B* 0 g 66 744.75 m 66 747.75 l 64.344 747.75 63 746.406 63 744.75 c 63 743.094 64.344 741.75 66 741.75 c 67.656 741.75 69 743.094 69 744.75 c 69 746.406 67.656 747.75 66 747.75 c f 1 G 0.33 w 69 744.75 m 63 744.75 l B* 66 741.75 m 66 747.75 l B* 1 g 546 744.75 m 546 750.75 l 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c f 0 G 0.27 w 546 750.75 m 542.688 750.75 540 748.062 540 744.75 c 540 741.438 542.688 738.75 546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 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546 738.75 c 549.312 738.75 552 741.438 552 744.75 c 552 748.062 549.312 750.75 546 750.75 c s 555 744.75 m 522 744.75 l B* 546 735.75 m 546 762.75 l B* 0 g 546 744.75 m 546 747.75 l 544.344 747.75 543 746.406 543 744.75 c 543 743.094 544.344 741.75 546 741.75 c 547.656 741.75 549 743.094 549 744.75 c 549 746.406 547.656 747.75 546 747.75 c f 1 G 0.33 w 549 744.75 m 543 744.75 l B* 546 741.75 m 546 747.75 l B* 1 g 66 47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c f 0 G 0.27 w 36 83.25 m 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 73.938 42 77.25 c 42 80.562 39.312 83.25 36 83.25 c s 45 77.25 m 18 77.25 l B* 36 68.25 m 36 101.25 l B* 0 g 36 77.25 m 36 80.25 l 34.344 80.25 33 78.906 33 77.25 c 33 75.594 34.344 74.25 36 74.25 c 37.656 74.25 39 75.594 39 77.25 c 39 78.906 37.656 80.25 36 80.25 c f 1 G 0.33 w 39 77.25 m 33 77.25 l B* 36 74.25 m 36 80.25 l B* 1 g 576 714.75 m 576 720.75 l 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c f 0 G 0.27 w 576 720.75 m 572.688 720.75 570 718.062 570 714.75 c 570 711.438 572.688 708.75 576 708.75 c 579.312 708.75 582 711.438 582 714.75 c 582 718.062 579.312 720.75 576 720.75 c s 594 714.75 m 567 714.75 l B* 576 690.75 m 576 723.75 l B* 0 g 576 714.75 m 576 717.75 l 574.344 717.75 573 716.406 573 714.75 c 573 713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 743.859 571.99 742.755 c 571.99 741.651 572.886 740.755 573.99 740.755 c 575.094 740.755 575.99 741.651 575.99 742.755 c 575.99 743.859 575.094 744.755 573.99 744.755 c h 574.005 744.24 m 573.177 744.24 572.505 743.568 572.505 742.74 c 572.505 741.912 573.177 741.24 574.005 741.24 c 574.833 741.24 575.505 741.912 575.505 742.74 c 575.505 743.568 574.833 744.24 574.005 744.24 c h 573.99 743.755 m 573.438 743.755 572.99 743.307 572.99 742.755 c 572.99 742.203 573.438 741.755 573.99 741.755 c 574.542 741.755 574.99 742.203 574.99 742.755 c 574.99 743.307 574.542 743.755 573.99 743.755 c 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emphasis on statistically sophisticated forms of)Tj /F6 1 Tf 27.1522 0 TD (smoothing)Tj /F2 1 Tf 4.1122 0 TD ( when data is miss-)Tj -31.2644 -1.4444 TD (ing. Now that very large corpora are available, we use approaches like stupid backoff and)Tj T* (no longer worry as much about the smoothing model.)Tj 0 -2.2222 TD (Most of the complexity in the programs we studied in this chapter was due to the search)Tj 0 -1.4444 TD (strategy. We saw three classes of search strategy:)Tj /F6 1 Tf 0 -2.2222 TD (Exhaustive)Tj /F2 1 Tf 1.3333 -1.4445 TD (For shift ciphers, there are only 26 candidates; we can test them all.)Tj /F6 1 Tf -1.3333 -1.8889 TD (Guaranteed)Tj /F2 1 Tf 1.3333 -1.4444 TD (For segmentation, there are 2)Tj 6.75 0 0 6.75 256.51 560.05 Tm (n)Tj 9 0 0 9 260.64 556.75 Tm ( candidates, but most can be proved nonoptimal \(given)Tj -13.6267 -1.4444 TD (the independence assumption\) without examining them.)Tj /F6 1 Tf -1.3333 -1.8889 TD (Heuristic)Tj /F2 1 Tf 1.3333 -1.4444 TD (For full substitution ciphers, we cant guarantee weve found the best candidate, but)Tj T* (we can search a representative subset that gives us a good chance of finding the max-)Tj T* [(ima.)-272.6(For)-273.4(many)-272.9(problems,)-273.4(the)-272.7(majority)-273.2(of)-273.4(the)-272.7(work)-272.9(will)-273.2(be)-273(in)-273.2(picking)-272.5(the)-273.8(right)-272.3(function)]TJ T* (to maximize, understanding the topology of the search space, and discovering a good)Tj T* (order to enumerate the neighbors.)Tj -1.3333 -2.2222 TD [(If)-259.7(we)-260.5(are)-259.9(to)-259.9(base)-260.7(our)-259.5(models)-260.7(on)-259.7(large)-260.8(amounts)-259.7(of)-260.1(data,)-259.6(well)-259.9(need)-260.8(data)-259.9(that)-259.7(is)-260.8(readily)-259.8(avail-)]TJ 0 -1.4444 TD [(able)-235(in)-234.8(the)-234.9(wild.)]TJ /F6 1 Tf 8.18 0 TD (N)Tj /F2 1 Tf 0.7222 0 TD [(-gram)-235.1(counts)-234.9(have)-234.2(this)-234.5(property:)-234.8(we)-235(can)-235(easily)-234.6(harvest)-235.4(a)-234.4(trillion)-234.5(words)]TJ -8.9022 -1.4444 TD (of naturally occurring text from the Web. On the other hand, labeled spelling corrections)Tj T* (do not occur naturally, and thus we found only 40,000 of them. It is not a coincidence)Tj T* (that the two most successful applications of natural languagemachine translation and)Tj T* [(speech)-246.6(recognitionenjoy)-245.2(large)-246.3(corpora)-246.6(of)-245.7(examples)-246.3(available)-246.4(in)-246.6(the)-246(wild.)-246.1(In)-247(contrast,)-245.9(the)]TJ T* (task of syntactic parsing of sentences remains largely unrealized, in part because there is)Tj T* (no large corpus of naturally occurring parsed sentences.)Tj 0 -2.2222 TD (It should be mentioned that our probabilistic data-driven methodologymaximize the)Tj 0 -1.4444 TD [(probability)-274.3(over)-273.5(all)-274(candidatesis)-273.7(a)-273.3(special)-273.9(case)-274.8(of)-273.4(the)]TJ /F6 1 Tf 24.2089 0 TD (rational)Tj /F2 1 Tf 3.4978 0 TD [(data-driven)-273.2(methodology)]TJ -27.7067 -1.4444 TD [(maximize)-269.1(expected)-269.4(utility)-269.8(over)-269.1(all)-269.6(candidates.)-269.4(The)]TJ /F6 1 Tf 22.4611 0 TD [(expected)-242.5(utility)]TJ /F2 1 Tf 6.1244 0 TD [(of)-270.1(an)-269(action)-270.2(is)-269.7(its)-268.9(average)]TJ -28.5856 -1.4444 TD (value to the user over all possible outcomes. For example, a rational spelling correction)Tj T* [(program)-235.3(should)-235.6(know)-235.3(that)-235.2(there)-235.9(are)-235.4(some)-234.8(taboo)-235.8(naughty)-235.9(words,)-234.7(and)-235.2(that)-235.2(suggesting)-235.6(them)]TJ T* (when they were not intended causes embarrassment for the user, a negative effect that is)Tj T* (much worse than just spelling a word wrong. The rational program takes into account)Tj T* (both the probability that a word is correct or wrong, and the positive or negative value of)Tj T* (suggesting each word.)Tj 0 -2.2222 TD (Uncertain problems require good discipline in validation and testing. To evaluate a solu-)Tj 0 -1.4444 TD [(tion)-276.4(to)-276.6(an)-276.8(uncertain)-276.3(problem,)-275.7(one)-277.4(should)-275.6(divide)-277.2(the)-276(data)-276.5(into)-276.4(three)-275.9(sets:)-276.5(\(1\))-277.1(A)]TJ /F6 1 Tf 34.9456 0 TD (training)Tj /F2 1 Tf 3.5556 0 TD (set)Tj -38.5011 -1.4444 TD (used to build the probabilistic model. \(2\) A)Tj /F6 1 Tf 19.3378 0 TD (validation)Tj /F2 1 Tf 4.0567 0 TD ( set that the developer uses to evalu-)Tj -23.3944 -1.4444 TD [(ate)-259.2(several)-259.2(different)-258.5(approaches,)-258.7(seeing)-258.6(which)-259.9(ones)-258.4(score)-259.8(better,)-258.9(and)-258.5(getting)-259.4(ideas)-258.1(for)-258.9(new)]TJ T* [(algorithms.)-246.6(\(3\))-247.1(A)]TJ /F6 1 Tf 7.7978 0 TD (test)Tj /F2 1 Tf 1.5256 0 TD [(set,)-246.7(which)-247.6(is)-247.4(used)-246.2(at)-248.1(the)-247.1(end)-246.3(of)-247.9(development)-246.1(to)-247.7(accurately)-247.3(judge)-247.2(how)]TJ ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 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endobj 87 0 obj > /ExtGState > >> endobj 89 0 obj > stream 1 g /GS1 gs 1 i 0 0 612 792 re f BT /F1 1 Tf 7.5 0 0 7.5 90 96.4 Tm 0 g 0 Tc 0 Tw (242)Tj /F3 1 Tf 2.724 0 TD 0.2 Tc [(CHAPTER)-376.3(FOURTEEN)]TJ /F2 1 Tf 9 0 0 9 126 678.75 Tm 0 Tc (well the algorithm will do on new, unseen data. After the test set has been used once it)Tj 0 -1.4444 TD (ideally should be discarded, just as a teacher cannot give the same test twice to a class of)Tj T* (students. But in practice, data is expensive, and there is a trade-off between paying to)Tj T* [(acquire)-240.9(new)-240.7(data)-239.9(and)-240.8(reusing)-240.9(old)-240(data)-241(in)-241(a)-240(way)-240.2(that)-240.8(does)-241.2(not)-240(cause)-240.4(your)-240.3(model)-240.9(to)]TJ /F6 1 Tf 36.13 0 TD (overfit)Tj /F2 1 Tf 2.74 0 TD (to)Tj -38.87 -1.4444 TD [(the)-273.8(data.)-273(Note)-272.3(that)-274.1(the)-272.7(need)-273(for)-273.3(an)-273.4(independent)-272.4(test)-273.9(set)-273.5(is)-273(inherent)-272.5(to)-273.2(uncertain)-273(problems)]TJ T* (themselves, not to the type of solution chosenyou should use proper test methodology)Tj T* (even if you decide to solve the problem with ad hoc rules rather than a probabilistic)Tj T* (model.)Tj 0 -2.2222 TD (In conclusion, as more data is available online, and as computing capacity increases, I)Tj 0 -1.4444 TD (believe that the probabilistic data-driven methodology will become a major approach for)Tj T* (solving complex problems in uncertain domains.)Tj /F1 1 Tf 15 0 0 15 126 512.75 Tm [(Ackno)19(wledgments)]TJ /F2 1 Tf 9 0 0 9 126 493.75 Tm -0.0156 Tc 0.0001 Tw (Thanks to Darius Bacon, Thorsten Brants, Andy Golding, Mark Paskin, and Casey Whitelaw)Tj T* 0 Tc 0 Tw (for comments, corrections, and code.)Tj ET q 9 771.75 594 -751.5 re W n 1 G 0 J 0 j 0.75 w 3.86 M []0 d 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S 0 G 0.27 w 45 726.75 m 9 726.75 l 45 65.25 m 9 65.25 l 603 65.25 m 567 65.25 l 603 726.75 m 567 726.75 l 54 735.75 m 54 771.75 l 558 735.75 m 558 771.75 l 558 20.25 m 558 56.25 l 54 20.25 m 54 56.25 l S Q 1 g 77 744.75 166.3 -9 re f* BT /F7 1 Tf 7 0 0 7 78 738.75 Tm 0 g (,ch14.14922 Page 242 Thursday, June 25, 2009 2:34 PM)Tj ET 1 g 36 396 m 36 402 l 32.688 402 30 399.312 30 396 c 30 392.688 32.688 390 36 390 c 39.312 390 42 392.688 42 396 c 42 399.312 39.312 402 36 402 c 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47.25 m 66 53.25 l 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c f 0 G 0.27 w 66 53.25 m 62.688 53.25 60 50.562 60 47.25 c 60 43.938 62.688 41.25 66 41.25 c 69.312 41.25 72 43.938 72 47.25 c 72 50.562 69.312 53.25 66 53.25 c s 90 47.25 m 57 47.25 l B* 66 29.25 m 66 56.25 l B* 0 g 66 47.25 m 66 50.25 l 64.344 50.25 63 48.906 63 47.25 c 63 45.594 64.344 44.25 66 44.25 c 67.656 44.25 69 45.594 69 47.25 c 69 48.906 67.656 50.25 66 50.25 c f 1 G 0.33 w 69 47.25 m 63 47.25 l B* 66 44.25 m 66 50.25 l B* 1 g 546 47.25 m 546 53.25 l 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c f 0 G 0.27 w 546 53.25 m 542.688 53.25 540 50.562 540 47.25 c 540 43.938 542.688 41.25 546 41.25 c 549.312 41.25 552 43.938 552 47.25 c 552 50.562 549.312 53.25 546 53.25 c s 555 47.25 m 522 47.25 l B* 546 29.25 m 546 56.25 l B* 0 g 546 47.25 m 546 50.25 l 544.344 50.25 543 48.906 543 47.25 c 543 45.594 544.344 44.25 546 44.25 c 547.656 44.25 549 45.594 549 47.25 c 549 48.906 547.656 50.25 546 50.25 c f 1 G 0.33 w 549 47.25 m 543 47.25 l B* 546 44.25 m 546 50.25 l B* 1 g 36 714.75 m 36 720.75 l 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c f 0 G 0.27 w 36 720.75 m 32.688 720.75 30 718.062 30 714.75 c 30 711.438 32.688 708.75 36 708.75 c 39.312 708.75 42 711.438 42 714.75 c 42 718.062 39.312 720.75 36 720.75 c s 45 714.75 m 18 714.75 l B* 36 690.75 m 36 723.75 l B* 0 g 36 714.75 m 36 717.75 l 34.344 717.75 33 716.406 33 714.75 c 33 713.094 34.344 711.75 36 711.75 c 37.656 711.75 39 713.094 39 714.75 c 39 716.406 37.656 717.75 36 717.75 c f 1 G 0.33 w 39 714.75 m 33 714.75 l B* 36 711.75 m 36 717.75 l B* 1 g 36 77.25 m 36 83.25 l 32.688 83.25 30 80.562 30 77.25 c 30 73.938 32.688 71.25 36 71.25 c 39.312 71.25 42 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713.094 574.344 711.75 576 711.75 c 577.656 711.75 579 713.094 579 714.75 c 579 716.406 577.656 717.75 576 717.75 c f 1 G 0.33 w 579 714.75 m 573 714.75 l B* 576 711.75 m 576 717.75 l B* 1 g 576 77.25 m 576 83.25 l 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c f 0 G 0.27 w 576 83.25 m 572.688 83.25 570 80.562 570 77.25 c 570 73.938 572.688 71.25 576 71.25 c 579.312 71.25 582 73.938 582 77.25 c 582 80.562 579.312 83.25 576 83.25 c s 594 77.25 m 567 77.25 l B* 576 68.25 m 576 101.25 l B* 0 g 576 77.25 m 576 80.25 l 574.344 80.25 573 78.906 573 77.25 c 573 75.594 574.344 74.25 576 74.25 c 577.656 74.25 579 75.594 579 77.25 c 579 78.906 577.656 80.25 576 80.25 c f 1 G 0.33 w 579 77.25 m 573 77.25 l B* 576 74.25 m 576 80.25 l B* 1 g 38 742.75 m 38 750.76 l 33.578 750.76 29.99 747.172 29.99 742.75 c 29.99 738.328 33.578 734.74 38 734.74 c 42.422 734.74 46.01 738.328 46.01 742.75 c 46.01 747.172 42.422 750.76 38 750.76 c f 0 G 0.27 w 38.01 750.755 m 33.594 750.755 30.01 747.171 30.01 742.755 c 30.01 738.339 33.594 734.755 38.01 734.755 c 42.426 734.755 46.01 738.339 46.01 742.755 c 46.01 747.171 42.426 750.755 38.01 750.755 c s 0 g 38 742.75 m 38.349 750.752 l 38.233 750.757 38.117 750.76 38 750.76 c f 38 742.75 m 39.734 750.57 l 39.62 750.595 39.506 750.618 39.391 750.638 c f 38 742.75 m 41.065 750.15 l 40.958 750.195 40.849 750.237 40.74 750.277 c f 38 742.75 m 42.304 749.506 l 42.206 749.568 42.106 749.629 42.005 749.687 c f 38 742.75 m 43.411 748.656 l 43.326 748.734 43.238 748.811 43.149 748.886 c f 38 742.75 m 44.355 747.626 l 44.284 747.719 44.211 747.809 44.136 747.899 c f 38 742.75 m 45.105 746.449 l 45.051 746.552 44.995 746.654 44.937 746.755 c f 38 742.75 m 45.639 745.159 l 45.604 745.27 45.567 745.38 45.527 745.49 c f 38 742.75 m 45.941 743.796 l 45.926 743.911 45.909 744.026 45.888 744.141 c f 38 742.75 m 46.002 742.401 l 46.007 742.517 46.01 742.633 46.01 742.75 c f 38 742.75 m 45.82 741.016 l 45.845 741.13 45.868 741.244 45.888 741.359 c f 38 742.75 m 45.4 739.685 l 45.445 739.792 45.487 739.901 45.527 740.01 c f 38 742.75 m 44.756 738.446 l 44.818 738.544 44.879 738.644 44.937 738.745 c f 38 742.75 m 43.906 737.339 l 43.984 737.424 44.061 737.512 44.136 737.601 c f 38 742.75 m 42.876 736.395 l 42.969 736.466 43.059 736.539 43.149 736.614 c f 38 742.75 m 41.699 735.645 l 41.802 735.699 41.904 735.755 42.005 735.813 c f 38 742.75 m 40.409 735.111 l 40.52 735.146 40.63 735.183 40.74 735.223 c f 38 742.75 m 39.046 734.808 l 39.161 734.824 39.276 734.841 39.391 734.862 c f 38 742.75 m 37.651 734.748 l 37.767 734.743 37.883 734.74 38 734.74 c f 38 742.75 m 36.266 734.93 l 36.38 734.905 36.494 734.882 36.609 734.862 c f 38 742.75 m 34.935 735.35 l 35.042 735.305 35.151 735.263 35.26 735.223 c f 38 742.75 m 33.696 735.994 l 33.794 735.932 33.894 735.871 33.995 735.813 c f 38 742.75 m 32.589 736.844 l 32.674 736.766 32.762 736.689 32.851 736.614 c f 38 742.75 m 31.645 737.874 l 31.716 737.781 31.789 737.691 31.864 737.601 c f 38 742.75 m 30.895 739.051 l 30.949 738.948 31.005 738.846 31.063 738.745 c f 38 742.75 m 30.361 740.341 l 30.396 740.23 30.433 740.12 30.473 740.01 c f 38 742.75 m 30.059 741.704 l 30.074 741.589 30.091 741.474 30.112 741.359 c f 38 742.75 m 29.998 743.099 l 29.993 742.983 29.99 742.867 29.99 742.75 c f 38 742.75 m 30.18 744.484 l 30.155 744.37 30.132 744.256 30.112 744.141 c f 38 742.75 m 30.6 745.815 l 30.555 745.708 30.513 745.599 30.473 745.49 c f 38 742.75 m 31.244 747.054 l 31.182 746.956 31.121 746.856 31.063 746.755 c f 38 742.75 m 32.094 748.161 l 32.016 748.076 31.939 747.988 31.864 747.899 c f 38 742.75 m 33.124 749.105 l 33.031 749.034 32.941 748.961 32.851 748.886 c f 38 742.75 m 34.301 749.855 l 34.198 749.801 34.096 749.745 33.995 749.687 c f 38 742.75 m 35.591 750.389 l 35.48 750.354 35.37 750.317 35.26 750.277 c f 38 742.75 m 36.954 750.691 l 36.839 750.676 36.724 750.659 36.609 750.638 c f 1 g 574 742.75 m 574 750.76 l 569.578 750.76 565.99 747.172 565.99 742.75 c 565.99 738.328 569.578 734.74 574 734.74 c 578.422 734.74 582.01 738.328 582.01 742.75 c 582.01 747.172 578.422 750.76 574 750.76 c f 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 573.99 750.755 m 569.574 750.755 565.99 747.171 565.99 742.755 c 565.99 738.339 569.574 734.755 573.99 734.755 c 578.406 734.755 581.99 738.339 581.99 742.755 c 581.99 747.171 578.406 750.755 573.99 750.755 c h 574.005 750.24 m 569.865 750.24 566.505 746.88 566.505 742.74 c 566.505 738.6 569.865 735.24 574.005 735.24 c 578.145 735.24 581.505 738.6 581.505 742.74 c 581.505 746.88 578.145 750.24 574.005 750.24 c h 573.99 749.755 m 570.126 749.755 566.99 746.619 566.99 742.755 c 566.99 738.891 570.126 735.755 573.99 735.755 c 577.854 735.755 580.99 738.891 580.99 742.755 c 580.99 746.619 577.854 749.755 573.99 749.755 c h 573.99 749.255 m 570.402 749.255 567.49 746.343 567.49 742.755 c 567.49 739.167 570.402 736.255 573.99 736.255 c 577.578 736.255 580.49 739.167 580.49 742.755 c 580.49 746.343 577.578 749.255 573.99 749.255 c h 574.005 748.74 m 570.693 748.74 568.005 746.052 568.005 742.74 c 568.005 739.428 570.693 736.74 574.005 736.74 c 577.317 736.74 580.005 739.428 580.005 742.74 c 580.005 746.052 577.317 748.74 574.005 748.74 c h 573.99 748.255 m 570.954 748.255 568.49 745.791 568.49 742.755 c 568.49 739.719 570.954 737.255 573.99 737.255 c 577.026 737.255 579.49 739.719 579.49 742.755 c 579.49 745.791 577.026 748.255 573.99 748.255 c h 573.99 747.755 m 571.23 747.755 568.99 745.515 568.99 742.755 c 568.99 739.995 571.23 737.755 573.99 737.755 c 576.75 737.755 578.99 739.995 578.99 742.755 c 578.99 745.515 576.75 747.755 573.99 747.755 c h 574.005 747.24 m 571.521 747.24 569.505 745.224 569.505 742.74 c 569.505 740.256 571.521 738.24 574.005 738.24 c 576.489 738.24 578.505 740.256 578.505 742.74 c 578.505 745.224 576.489 747.24 574.005 747.24 c h 573.99 746.755 m 571.782 746.755 569.99 744.963 569.99 742.755 c 569.99 740.547 571.782 738.755 573.99 738.755 c 576.198 738.755 577.99 740.547 577.99 742.755 c 577.99 744.963 576.198 746.755 573.99 746.755 c h 573.99 746.255 m 572.058 746.255 570.49 744.687 570.49 742.755 c 570.49 740.823 572.058 739.255 573.99 739.255 c 575.922 739.255 577.49 740.823 577.49 742.755 c 577.49 744.687 575.922 746.255 573.99 746.255 c h 574.005 745.74 m 572.349 745.74 571.005 744.396 571.005 742.74 c 571.005 741.084 572.349 739.74 574.005 739.74 c 575.661 739.74 577.005 741.084 577.005 742.74 c 577.005 744.396 575.661 745.74 574.005 745.74 c h 573.99 745.255 m 572.61 745.255 571.49 744.135 571.49 742.755 c 571.49 741.375 572.61 740.255 573.99 740.255 c 575.37 740.255 576.49 741.375 576.49 742.755 c 576.49 744.135 575.37 745.255 573.99 745.255 c h 573.99 744.755 m 572.886 744.755 571.99 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