This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2000.4.27) 16 NOV 2005 14:18 **notes2805 (notes2805.tex LaTeX2e <1999/12/01> patch level 1 Babel and hyphenation patterns for american, french, german, ngerman, n ohyphenation, loaded. (/usr/local/teTeX/share/texmf/tex/latex/base/book.cls Document Class: book 1999/09/10 v1.4a Standard LaTeX document class (/usr/local/teTeX/share/texmf/tex/latex/base/bk12.clo File: bk12.clo 1999/09/10 v1.4a Standard LaTeX file (size option) ) \c@part=\count79 \c@chapter=\count80 \c@section=\count81 \c@subsection=\count82 \c@subsubsection=\count83 \c@paragraph=\count84 \c@subparagraph=\count85 \c@figure=\count86 \c@table=\count87 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (/usr/local/teTeX/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 1996/11/03 v2.2b (/usr/local/teTeX/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \@emptytoks=\toks14 \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 133. )) (/usr/local/teTeX/share/texmf/tex/latex/base/latexsym.sty Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols) \symlasy=\mathgroup6 LaTeX Font Info: Overwriting symbol font `lasy' in version `bold' (Font) U/lasy/m/n --> U/lasy/b/n on input line 42. ) (/usr/local/teTeX/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/01/15 v2.05 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. 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(/usr/local/teTeX/share/texmf/tex/latex/base/ulasy.fd File: ulasy.fd 1998/08/17 v2.2eLaTeX symbol font definitions ) LaTeX Font Info: Try loading font information for OMS+cmtt on input line 110 . LaTeX Font Info: No file OMScmtt.fd. on input line 110. LaTeX Font Warning: Font shape `OMS/cmtt/m/n' undefined (Font) using `OMS/cmsy/m/n' instead (Font) for symbol `textbraceleft' on input line 110. [1 ] [2] (notes2805.toc) \tf@toc=\write4 \openout4 = `notes2805.toc'. (Preface.tex [3 ] [4 ] LaTeX Font Info: Try loading font information for OMS+cmr on input line 16. (/usr/local/teTeX/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 16. ) [5] [6 ] (ChapterIntroduction.tex Chapter 1. [1 ] [2] [3] [4] [5] (FIGS/graph-example.ipe) [6] Overfull \hbox (4.09409pt too wide) in paragraph at lines 249--261 [][] [] [7] [8] [9] [10] [11] [12] [13] [14] [15] Overfull \hbox (3.96707pt too wide) in paragraph at lines 722--731 [][] [] Underfull \hbox (badness 10000) in paragraph at lines 722--731 [] [16] [17] [18] (FIGS/planar.ipe) [19] [20] [21] Overfull \hbox (50.70749pt too wide) in paragraph at lines 1070--1073 []\OT1/cmr/m/n/12 Show that the set of func-tions from pos-i-tive in-te-gers to the set \OMS/cmsy/m/n/12 f\OT1/cmr/m/n/12 0,1,2,3,4,5,6,7,8,9\OMS/cmsy/m/n/12 g [] ) (ChapterRegular.tex [22] Chapter 2. [23 ] (FIGS/toll-fsa.ipe) (FIGS/even0-DFA.ipe) [24] [25] Overfull \hbox (1.2844pt too wide) in paragraph at lines 137--144 \OT1/cmr/m/n/12 toma-ton. For this ex-am-ple, we have $\OML/cmm/m/it/12 Q \OT1/ cmr/m/n/12 = \OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 q[]; q[]; q[]; q[]; q[]; q[]\OM S/cmsy/m/n/12 g$\OT1/cmr/m/n/12 , $^^F = \OMS/cmsy/m/n/12 f\OT1/cmr/m/n/12 5\OM L/cmm/m/it/12 ; \OT1/cmr/m/n/12 10\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 25\OMS/cms y/m/n/12 g$\OT1/cmr/m/n/12 , [] Overfull \hbox (11.46263pt too wide) detected at line 179 \OML/cmm/m/it/12 L\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 M\OT1/cmr/m/n/12 ) = \OMS/c msy/m/n/12 f\OML/cmm/m/it/12 w \OT1/cmr/m/n/12 : []\OMS/cmsy/m/n/12 g\OML/cmm/m /it/12 : [] [26] [27] [28] (FIGS/odd-even-FA.ipe) [29] (FIGS/101-DFA.ipe) [30] [31] [32] [33] [34] (FIGS/NFA1.ipe) [35] (FIGS/NFA1paths7.ipe) [36] (FIGS/NFA2.ipe) [37] Overfull \hbox (17.37529pt too wide) in paragraph at lines 713--717 \OT1/cmr/m/n/12 The start state is $\OML/cmm/m/it/12 q[]$\OT1/cmr/m/n/12 , and the set of ac-cept states is equal to $\OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 q[]; q[]; q[]; q[]\OMS/cmsy/m/n/12 g$\OT1/cmr/m/n/12 . [] (FIGS/DFA2.ipe) [38] (FIGS/NFA3.ipe) [39] [40] [41] [42] [43] (FIGS/nfadfa.ipe) [44] (FIGS/nfadfa1.ipe) [45] (FIGS/nfadfa2.ipe) [46] [47] (FIGS/union.ipe) Overfull \hbox (52.86552pt too wide) in paragraph at lines 29--1120 [] [] Overfull \vbox (1.24896pt too high) has occurred while \output is active [] [48] (FIGS/concat.ipe) [49] (FIGS/star.ipe) Overfull \hbox (25.88974pt too wide) in paragraph at lines 28--1211 [] [] [50] [51] [52] Overfull \hbox (0.95715pt too wide) in paragraph at lines 1320--1323 []\OT1/cmr/m/n/12 The lan-guage $\OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 w \OT1/cmr/ m/n/12 : []\OMS/cmsy/m/n/12 g$ \OT1/cmr/m/n/12 is de-scribed [] [53] [54] Overfull \hbox (11.8138pt too wide) in paragraph at lines 1436--1436 []\OT1/cmr/bx/n/17.28 Equivalence of reg-u-lar ex-pres-sions and reg- [] Overfull \hbox (70.94553pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 2.8. EQUIVALENCE OF REGULAR EXPRESSIONS AND REGULAR LANGUAGES \OT1/cmr/m/n/12 55 [] [55] (FIGS/base1.ipe) (FIGS/base2.ipe) (FIGS/base3.ipe) [56] (FIGS/M1.ipe) Overfull \hbox (70.94553pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 2.8. EQUIVALENCE OF REGULAR EXPRESSIONS AND REGULAR LANGUAGES \OT1/cmr/m/n/12 57 [] [57] (FIGS/M2.ipe) (FIGS/M3.ipe) (FIGS/M4.ipe) (FIGS/M5.ipe) Overfull \hbox (10.79988pt too wide) in paragraph at lines 29--1612 [] [] [58] Overfull \hbox (70.94553pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 2.8. EQUIVALENCE OF REGULAR EXPRESSIONS AND REGULAR LANGUAGES \OT1/cmr/m/n/12 59 [] [59] [60] Overfull \hbox (70.94553pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 2.8. EQUIVALENCE OF REGULAR EXPRESSIONS AND REGULAR LANGUAGES \OT1/cmr/m/n/12 61 [] [61] (FIGS/dfare.ipe) Underfull \vbox (badness 4899) has occurred while \output is active [] [62] Overfull \hbox (70.94553pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 2.8. EQUIVALENCE OF REGULAR EXPRESSIONS AND REGULAR LANGUAGES \OT1/cmr/m/n/12 63 [] [63] [64] (FIGS/pumping.ipe) Underfull \vbox (badness 1460) has occurred while \output is active [] [65] [66] [67] [68] [69] (FIGS/equal0110.ipe) [70] [71] (FIGS/exnfadfa.ipe) (FIGS/exdfare.ipe) [72] [73] [74] Overfull \hbox (15.30699pt too wide) in paragraph at lines 2423--2425 []\OT1/cmr/m/it/12 Show that if $\OML/cmm/m/it/12 L$ \OT1/cmr/m/it/12 is reg-u- lar than so is $\OML/cmm/m/it/12 L[]$\OT1/cmr/m/it/12 , where $\OML/cmm/m/it/12 L[] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 c\OMS/cmsy/m/n/12 j9\ OML/cmm/m/it/12 a; b[]; \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 a\OMS/cmsy/m/n/12 j \OT1/cmr/m/n/12 = [] [75]) (ChapterContextfree.tex [76] Chapter 3. [77 ] (FIGS/parse-tree.ipe) [78] Overfull \hbox (2.8773pt too wide) in paragraph at lines 134--137 []\OT1/cmr/m/n/12 A lan-guage $\OML/cmm/m/it/12 L$ \OT1/cmr/m/n/12 is called \O T1/cmr/m/it/12 context-free\OT1/cmr/m/n/12 , if there ex-ists a context- [] [79] [80] Overfull \hbox (22.92195pt too wide) in paragraph at lines 191--194 []\OT1/cmr/m/n/12 In a sym-met-ric way, we see that the context-free gram-mar $ \OML/cmm/m/it/12 G[] \OT1/cmr/m/n/12 = (\OML/cmm/m/it/12 V[]; \OT1/cmr/m/n/12 ^ ^F\OML/cmm/m/it/12 ; R[]; S[]\OT1/cmr/m/n/12 )$, [] [81] Overfull \hbox (11.08582pt too wide) in paragraph at lines 287--290 []\OT1/cmr/m/n/12 We ob-tain the context-free gram-mar $\OML/cmm/m/it/12 G \OT1 /cmr/m/n/12 = (\OML/cmm/m/it/12 V; \OT1/cmr/m/n/12 ^^F\OML/cmm/m/it/12 ; R; S\O T1/cmr/m/n/12 )$, where $\OML/cmm/m/it/12 V \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 S; A; B\OMS/cmsy/m/n/12 g$\OT1/cmr/m/n/12 , [] [82] [83] [84] (FIGS/101-DFA2.ipe) [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] Overfull \hbox (34.17111pt too wide) in paragraph at lines 1018--1020 []\OT1/cmr/m/n/12 We now spec-ify the com-pu-ta-tion of the push-down au-toma-t on $\OML/cmm/m/it/12 M \OT1/cmr/m/n/12 = (^^F\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 ^^@\OML/cmm/m/it/12 ; Q; ^^N; q\OT1/cmr/m/n/12 )$. [] [96] Overfull \hbox (3.6065pt too wide) in paragraph at lines 1038--1040 \OT1/cmr/bx/n/12 Acceptance: \OT1/cmr/m/n/12 The push-down au-toma-ton \OT1/cmr /m/it/12 ac-cepts \OT1/cmr/m/n/12 the in-put string $\OML/cmm/m/it/12 a[]a[] [] a[] \OMS/cmsy/m/n/12 2 [] [97] Overfull \hbox (4.6429pt too wide) in paragraph at lines 1117--1138 [][] [] [98] [99] Underfull \vbox (badness 2662) has occurred while \output is active [] [100] Overfull \hbox (108.72145pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 3.7. EQUIVALENCE OF PUSHDOWN AUTOMATA AND CONTEXT-FREE GRAMMA RS \OT1/cmr/m/n/12 101 [] [101] [102] Overfull \hbox (108.72145pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 3.7. EQUIVALENCE OF PUSHDOWN AUTOMATA AND CONTEXT-FREE GRAMMA RS \OT1/cmr/m/n/12 103 [] [103] [104] Overfull \hbox (108.72145pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 3.7. EQUIVALENCE OF PUSHDOWN AUTOMATA AND CONTEXT-FREE GRAMMA RS \OT1/cmr/m/n/12 105 [] [105] Overfull \hbox (1.42787pt too wide) in paragraph at lines 1566--1570 []\OT1/cmr/m/it/12 Let [] [106] (FIGS/pumpingCFL.ipe) Overfull \hbox (7.06035pt too wide) in paragraph at lines 37--1635 [] [] Underfull \vbox (badness 7326) has occurred while \output is active [] [107] [108] [109] [110] [111] [112] [113] Overfull \hbox (34.06566pt too wide) in paragraph at lines 1958--1965 [][] [] [114] Overfull \hbox (158.7891pt too wide) in paragraph at lines 2033--2035 []$\OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 w \OMS/cmsy/m/n/12 2 f\OML/cmm/m/it/12 a; b\OMS/cmsy/m/n/12 g[] \OT1/cmr/m/n/12 : []\OMS/cmsy/m/n/12 g$ [] Overfull \hbox (39.33775pt too wide) in paragraph at lines 2044--2049 []$\OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 w\OT1/cmr/m/n/12 #\OML/cmm/m/it/12 x\OMS/ cmsy/m/n/12 j[]g$\OT1/cmr/m/n/12 . For ex-am-ple, $\OML/cmm/m/it/12 aba\OT1/cmr /m/n/12 #\OML/cmm/m/it/12 abbababbb$ [] [115] LaTeX Font Info: Font shape `OMS/cmr/m/it' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 2072. ) (ChapterTuring.tex [116] Chapter 4. [117 ] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 118 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [118] Overfull \hbox (94.15196pt too wide) in paragraph at lines 117--119 []\OT1/cmr/m/n/12 A \OT1/cmr/m/it/12 de-ter-min-is-tic Tur-ing ma-chine \OT1/cm r/m/n/12 is a 7-tuple $\OML/cmm/m/it/12 M \OT1/cmr/m/n/12 = (^^F\OML/cmm/m/it/1 2 ; \OT1/cmr/m/n/12 ^^@\OML/cmm/m/it/12 ; Q; ^^N; q; q[]; q[]\OT1/cmr/m/n/12 )$ , [] [119] Overfull \hbox (71.47594pt too wide) in paragraph at lines 176--178 []\OT1/cmr/m/n/12 We now spec-ify the com-pu-ta-tion of the Tur-ing ma-chine $\ OML/cmm/m/it/12 M \OT1/cmr/m/n/12 = (^^F\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 ^^@\ OML/cmm/m/it/12 ; Q; ^^N; q; q[]; q[]\OT1/cmr/m/n/12 )$. [] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 120 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [120] Overfull \hbox (19.83215pt too wide) detected at line 270 [] [] [121] Underfull \vbox (badness 10000) has occurred while \output is active [] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 122 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [122] [123] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 124 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [124] [125] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 126 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [126] [127] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 128 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [128] [129] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 130 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [130] [131] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 132 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [132]) (ChapterDecidable.tex [133] Overfull \hbox (29.66937pt too wide) has occurred while \output is active \OT1/cmr/m/n/12 134 \OT1/cmr/m/sl/12 CHAPTER 4. TURING MACHINES AND THE CHURCH -TURING THESIS [] [134 ] Chapter 5. [135] Overfull \hbox (46.2992pt too wide) detected at line 85 [] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 fh\OML/cmm/m/it/12 p\OMS/cmsy/m/n/12 i \O T1/cmr/m/n/12 : []\OMS/cmsy/m/n/12 g [] [136] [137] Overfull \hbox (44.1849pt too wide) detected at line 168 \OML/cmm/m/it/12 A[] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 fh\OML/cmm/m/it/12 M; w \OMS/cmsy/m/n/12 i \OT1/cmr/m/n/12 : []\OMS/cmsy/m/n/12 g\OML/cmm/m/it/12 : [] [138] Overfull \hbox (63.0097pt too wide) detected at line 203 \OML/cmm/m/it/12 A[] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 fh\OML/cmm/m/it/12 M; w \OMS/cmsy/m/n/12 i \OT1/cmr/m/n/12 : []\OMS/cmsy/m/n/12 g\OML/cmm/m/it/12 : [] [139] [140] [141] [142] [143] [144] [145] [146] [147] Overfull \hbox (11.13957pt too wide) detected at line 682 [] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 fh\OML/cmm/m/it/12 P; w\OMS/cmsy/m/n/12 i \OT1/cmr/m/n/12 : []\OMS/cmsy/m/n/12 g\OML/cmm/m/it/12 : [] [148] [149] [150] Overfull \hbox (76.48991pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 5.6. THE RELATION BETWEEN DECIDABLE AND ENUMERABLE LANGUAGES \OT1/cmr/m/n/12 151 [] [151] [152] [153] [154]) (ChapterComplexity.tex [155] [156 ] Chapter 6. [157] [158] [159] (FIGS/2farb.ipe) [160] [161] [162] [163] [164] Overfull \hbox (2.95879pt too wide) in paragraph at lines 471--473 []\OT1/cmr/m/n/12 Consider the sum of sub-set prob-lem. A so-lu-tion is a se-qu ence $\OML/cmm/m/it/12 c[]; c[]; [] ; c[]$\OT1/cmr/m/n/12 . [] [165] [166] [167] [168] [169] [170] [171] Overfull \hbox (10.13788pt too wide) in paragraph at lines 839--843 []\OT1/cmr/m/n/12 Let us as-sume that $\OMS/cmsy/m/n/12 h\OML/cmm/m/it/12 a[]; a[]; [] ; a[]; b\OMS/cmsy/m/n/12 i 2 []$\OT1/cmr/m/n/12 . Then there are $\OML/ cmm/m/it/12 c[]; c[]; [] ; c[] \OMS/cmsy/m/n/12 2 [] [172] [173] [174] Overfull \hbox (3.71681pt too wide) in paragraph at lines 1023--1029 [][] [] [175] Overfull \hbox (21.21892pt too wide) in alignment at lines 1069--1082 [][][] [] [] [176] [177] (FIGS/graph.ipe) [178] [179] [180] [181] [182] [183] [184] (FIGS/rahmen.ipe) [185] Overfull \vbox (3.17966pt too high) has occurred while \output is active [] [186] [187] [188] LaTeX Warning: `h' float specifier changed to `ht'. LaTeX Warning: `h' float specifier changed to `ht'. [189] [190] [191] [192] [193] [194] [195]) (ChapterSummary.tex [196] [197] [198] Chapter 7. [199 ] [200] [201] [202] [203] (FIGS/summary.ipe) Overfull \hbox (57.8264pt too wide) in paragraph at lines 26--187 [] [] ) [204] (notes2805.aux) LaTeX Font Warning: Some font shapes were not available, defaults substituted. LaTeX Warning: There were multiply-defined labels. ) Here is how much of TeX's memory you used: 1810 strings out of 10901 19418 string characters out of 72188 91595 words of memory out of 263001 4645 multiletter control sequences out of 10000+0 25363 words of font info for 99 fonts, out of 400000 for 1000 14 hyphenation exceptions out of 1000 27i,13n,24p,309b,460s stack positions out of 300i,100n,500p,50000b,4000s Output written on notes2805.dvi (210 pages, 568504 bytes).