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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX6 %!PS-AdobeFont-1.1: CMBX6 1.0 %%CreationDate: 1991 Aug 20 16:35:30 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-49 -250 1367 753}readonly def /UniqueID 5000764 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F05C11F9A72F5DA508C30BC4BF52C8B1EC5FB 7F9DDDD0964A6D591DFD9EADB67720E5596FA8FBC900296430DED80E17C9C632 C6D81D798EACEE7FE9DD03BB1D083103B504E110AE2A98433FF946B31A9BD010 E531EE48EA92102FC8E1A26D47BE7D613724AB2DA99F90444388FB6828EF2D22 9D97902D566E2F3E9D83F4A88315338D5DBB3C596DBB8026293C2AAAA6E1EA81 2D3A6B6E63BB9BD579F33E12B666757E9C6885DF78FB8571316F7270ED2DE22A 94F2580A51382C23282C5F560063F6E55031F2E5EE94EB4C6E6A83FE65B846AB DC03417F00E3F923D48041C9A5D891296186EF575D80C5C2954D549D09BB6BE2 6E9F1947619D7CACA8059B516E8FF7D38C3D5F8FAD15618DAF9570675B54460C 5C0B6C929FFA36E49463AF53B519407A648644BCD5C65194C2551BC224F574E4 97F0BF4511C29DE9ECE6D9283F067D061274B3543695BFDE08680244AEBB5DDD 65B7ECE0FD9E23E1F82A845295A31081410135D4111C337C95B1820839E82947 44B6E99C76EF2A6C082363FC40C460A76EEC8C9E0D9E95496D27371B680C4C97 9B6267975FEB4770EB8EE55D4BBABD079CB8856B686AD789DA5B56920A475C99 88BC15BE2D97354CDDB3F529461F09594E9FDE6401B5FEBCE8D804E2BC8433B8 1E87DB162C037A4611B558070F9F7F79F8AFF124EF1033C2AEC73A608C4E4A21 8E7695DF125281E0C45F6C5921B16D6725DF67943B6C68829082D1E03956309E CAAA93185582014C37C4E6E945A572773B0B0A2D76EE5B168F047E5931044903 70E65092B2E166BBC365D3994AC89B211985D09A3D08ED8B15ECE9FC22454043 D18BA678DE6618940B338101A8F395F1912E89BB616AD7E664D04747A5A0B7AF F0266093EDB7B6A33FAB23B2455EAEE839F3FB3994B8513151A787F239A7692C E81F8657858DEFFF56D8ED523EEE6262011F6C06BB8C4B59B0459CE1E2219792 393C8ADACAB8A3C7FEC34A52EDC7DF47F673B29D6706437342D953D68EAA6830 31DB34325D78BADDA9BBE72D20F3D6A4A9F36F3CBC83BC186B9EEBB9407BD886 5C2D2455119A0FB67101620FABA419AE414B144049F4794BBB0948461D364769 8A7CD9D41197EF433019F589E808771658609A3EA94B8560DEC0698991FE5516 561EB568E34EBB87789B39AD2032A42CAF27AB504347062BAE8CF04F6E96D3D2 83D0918DADC1B126C197936755E9E8CF22B3A3F1DA91F299A05DFA85A76C834C 49CC15EBE24EBE46E9FE317E2E47BEE58B767AFED5D1E583F83BB0C32B4F71CF C2A3840C68AEE359ECD402D250016D504DD7A5245BC03D05771A1A9249FBF869 B52D9B10D286333F2E4DB6EF67EAC0FFCF9292851BF7AF23DD92D124C4C47678 7133F165D573B231DF15D05FEE35C14DE9691F742CC468A2908E3008101760D9 8259506B735ADAE1FA2660C7282C92B03121B32F77473E2E06553014A1AC714F 297607FDB234FE4519DE8FE4BCF94C19395D71FE8A46DB0D8D0C750ACCFCBBD9 EA08D9949F2E0199D5A225C140C7471D66C368C4BA90EFC377403B55E7FFEDC3 EB2391BB35E54A667EE97DE8CDEF1227A5BA86DB8D75A3E259108C72C6C7846E 34AD4592C40B98A70A3044F0B025E6F83386762B437BEC2AEE00E9E917EE02DE 98129ACAEE5892B8319052BEB36359874A5B37D694BE85FDA43467BA613BAFF5 9DB0824AD8FB6BF19050C80A7FD30AECD923645E327EA1EF1C697FAF05760670 CE9179546BB7354C25BC76FD1250B8772DAA16C2E1CF53E3629ECD2B0DF914BA F7A478C81C6789D1999B7BF567FAB35F7AD5871AAB74A34B846BFEDC699614DC 88840B1E99D3ED3B0B00C089E46AC7D38BB60270A07853FC1AD603C52684E47E D0164EDDE86E1C92377783505ABDB5B28DF4C84BA3EE10D8394D3C416AEC5E16 0F2FEAAF901278797E831849CAAABF8FDE7D407DB8DFEFA307DF21CC3EB8040C EBD308FE008CDFB8F386AC860967391297A93AFA8B604F0B 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX8 %!PS-AdobeFont-1.1: CMBX8 1.0 %%CreationDate: 1991 Aug 20 16:36:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F05C11F9A72F5DA508C30BC4BF52C8B1EC5FB 7F9DDDD0964A6D59193A389D490DAA6F6ACD02CF71C06802F3AE5A001F2B3A6D 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 8 /braceleftbig put dup 9 /bracerightbig put dup 83 /uniontext put dup 88 /summationdisplay put dup 91 /uniondisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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39925C10B533D04B59BBE16031CABC24E49405FD5F731F82551D55A075C7AEEA 6FCA65A34958577779B54F4ED46BAD9D5603E610518D99911A01D81AFE907D11 6A78F45DB3A4D96BB9567D3B85E0A1D8BED10709254E808E315C7914A5F312F6 4541B7D285A8F31C81673EFDFA94D04B5AC22E129BC5EB902FC0C4335B2762CD D81DEEA31B53951475A58504EA3283C642B3455378560166599BF0563C453677 A1C18620D66CBBE9D59C15669F44B289F699FE2F52921F26412A5BF298DC704A 3C3BEC6CA947B7EFB0DD175F07A3620AF948B79469A109F22B9D4A427F0311E4 3671F014E6C12BAA30DA0BB7E28E384EBFEB635D7255D78BB84396C2FCF23B13 FB0BB6F0AC23C76734A6A2BFD927B2B1C92580003811A89A4370CBA2A5D647FB 970AF17AE481EA2F8401E85157A9473E465D7C3D2C9468F7001BE04267F0ECD3 7A3D3FDBEC3BCF7357E6C3A3EB95202DD2093B2079D0E67B2B60E183BFFA52B1 3F56315057B1C46D0CE531BDE37C5E5E517A81482E56C7F7A9180E410A7FE051 0EB453793D652B8BFF0A334E56A6503F1AE26E138A9FF5B93495B8B6A283B75E 0634C6BEAC94D71384B3846F461BB94F9BF1A7DD699F56D6B82DCFFD6EA9246A 7F611F493A3471CD8A0E65808C5951CD77D0B05B98A984E1574980CFBFF9E775 00182CA187DD8C8E95D21D0CF4A486A079871CBAF94D518A87729EEEF6E64302 70B6267EDD0BEAE6EC7096693DD252C4EA4FB47C5EFEF5295A80FF47943EA15A 2E6DED9CCB94AD8394378D6D70A53667C9755283F1CFD6D9DF8BF3A2 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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%%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 78 /N put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 D10F04E2C2822D3E73F25B81C424627D3D9A158EAB554233A25D3C6849ABA86F 1F25C1667CB57D2E79B7803083CB7CC0616467F68450D9A3FEAB534EB9721003 DBFEEFD050F3AC3492F5C74162A9A531ECEC0F47610B4940E946D21CAA771D30 A6C27ECBA11708CC46C62396BF9D1990D579D0C394899D24FE7A4382EA18E7E1 160E7283AF5BE17254790628E79FCC206F28B5566075B3A5697D5209062544FF D85FD89D6F43D6588B242AB2666B5D2861CD38A8CE676503EDFAE84D12A71E77 8405E468FE391F4F3F50D2C57ED55512036B0DB8E76A7EF413ED08673E56DE2C 16A3B65CD478433C0D2F9FEC4E662D54DAA43CFA6957D2A9AF8979BE06F70B68 ED4C8C493D6DAC4971A3F1D010A7726D084EC1074FECD7D12D72AE16C26194AF 21AF5774D9B860EEE8608D34F150092F09C19959BAA670022B9A9F263CD391E3 74DD1D1B4CD4D75273CAA4E37F68C631723E08FA35AD34C0AFB4621AE6689861 854D16CE1C375FD159A337E221A6FF1CFFB5693A0623E7EBB58C2969F590D081 AD92DD9E5322E26D6A15023664AC73A355998BCC48ADD0E7A4BC79790519606F A1FEF6075033BCD1A542ED2F7EE4943A13D927138CB26A52F33F52249DD24930 BBA9773D5DEB5B8115804C2E65EDBCCB17469C47F2591BB232690DAC5F1780A5 6FE9861DC450426725D35E3E8006C022026C0A383B0A6E8AA30A52055E7E139B DF6ABC491AF90C7A3884582B7407C0DDF37CC49F3CBA0126D07A3639A615400A 01FC5412668335BC7FB0C5C62F533276BC13716EA27CCD3924408650605BEEDE 2A68B5B6105D8766B9DD6A877DE6AEA9C3179677B7C0726022D0F929E7E63574 4692A959C7B4919DEC77FA5012A3CB81439F809D15DA7739FAB5D8E03BD8F283 FB6832C9864D18C4CD499B20534D33C822226FC199D26116A73ABA2B5CAB0B63 42F1B4A3003688088F1F6DA3C61363B4C0C44269FD21F981DA0BDC5D180FFD2C 8BAB61F4330FE5806A35F1235364554FAA1CA61EC79EB01793D586FB1B62F4E9 3FA5AF30C87F9092E25245CBEEC03795B45CAE8D0664440E5D398D9167970E71 B0A2049EEADDBB2640950005BD22D2494E418F56F9855215A354EEC605D83261 1509734FB628707CBBB28FCA313ADE564D964B20EF6EB71A598FCD66DA81BA11 F320B05D0224E0F37018CE45ABC95F653E003DFF2E7EBC5EC2DE839BF35DD55E 3D9B293AADE0A79D26253459D2AFEA3C6C7283CB47CF4C2427B5F45D27F82EB6 20101042F749852BC16ADE5B10519C24D4B768511AF0584B059AA6040F130661 FC7A4CA84FF55BA1C88C641E424A109A2497BE459FA57CBAA9FD894EDED81724 CCD5EE776012834E453FCBC122A551266E3DE64578E1738DA6BB01F21F955110 4B44CAA2E7ED6A059153030015257D51F49666B04C574427E54ECCF82B8EC2B3 63ADF00A511556B0E6990369430C12760A9D00A4CFEC8656651355D65F611293 8F2AF1B1004A1E0EFCEB487ABF7C5AF5CF88DB9EB5AC94BEB2B2E052E7F937AF 3DF019367FE9EB63070517BA251E615475B57635BF685959638BE01DC95CCDEF 99B9D3B5CD6CD3F1F38E97B680988E44EC6A86553CFC634DB2269C3A06EB417C EBFB9F7BFF1CE39733010688015E5B67F3A2B5C8906C624FE25BF4F0FE91C492 12253EFF1113FACA2048C5169DD3478E0675A5C7F62518EAE05C359F04095C5D 3EAEA5358DA086D0AC996066A1434C55A02A7265855D7D4BC94B98EC6F7DB275 8EBA4245E7A8B344DE9D65D23C5D19E5504E086C065E943DE6D94DB03E67654F 1FB395EC4B8898770EF3DF5E6971D57DC09D42D274AA5D1A606DF6AF52DCDF25 446987CEF533FF4F40A8EB4A33A84B0C9FD510732C6A1B610ECB3BB4576F171A 7501BA91FA3DF6F12696A0A872332223F4DEF7057B67960E3A0BAA23BF5139CD B6CFBC323D5F491FDDA0D277E6434152DE1A291E815FFA68458EABD2D1942D14 74B565ACB042BE0E13C9B2358B61EE7C6000498F809C68D96D9218CE48A2987F 03764848D7F01B0C31C461D7836774A9CE439D749A4B1ADA5F7907D49AE3018F E8BD71FDC157B542393D98BA014FAD7861D6E1B32AA7D7FDDB2BC6C52FECA0A3 5BC7B355D6A81D04230FDD94F50CB785E6224D8731231C38DC6D9C61E4E29C79 982C2EF103477EAE8E197D98B00DBCEC47713C6B07B26B473B4621DA06E7B46D C85A4EE0F8DF8C20C8A2FC62EAD53E8AD1D4AD1526B799D20A4800164318FDBE BF268A013FDFFA39AF3A1F3202C35D01C371BE0B0FFE56114D9D697BDCCCA62C E6E6EB6CC697BF80EFEF 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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b(a)h(function)h FJ(t)41 b FI(:)83 4098 y FJ(X)33 b FH(!)25 b(f)r FE(T)t(R)q(U)t(E)5 b FJ(;)17 b FE(F)o(A)t(L)t(S)t(E)5 b FH(g)p FK(.)29 b(Basically)-6 b(,)25 b FJ(t)e FK(assigns)i(to)f(each)g(v)n(ariable)i(in)d FJ(X)31 b FK(a)23 b(v)n(alue)h(of)g(either)j FE(T)t(R)q(U)t(E)g FK(or)e FE(F)o(A)t(L)t(S)t(E)6 b FK(.)28 b(F)o(or)23 b(a)83 4211 y(v)n(ariable)i FJ(x)p FK(,)e(we)f(use)30 b FI(\026)-51 b FJ(x)23 b FK(to)g(denote)j(the)d(ne)o(gation)i(of)f FJ(x)p FK(.)k(If)23 b FJ(x)g FK(is)g(a)g(v)n(ariable,)i FJ(x)e FK(and)30 b FI(\026)-51 b FJ(x)22 b FK(are)i(called)h FF(liter)o(als)p FK(.)224 4324 y(A)d(set)h FJ(C)29 b FK(of)22 b(literals)j(o)o(v)o(er)e FJ(X)30 b FK(is)22 b(called)i(a)f FF(clause)h FK(o)o(v)o(er)f FJ(X)7 b FK(,)23 b(e.g.)28 b FJ(C)k FI(=)25 b FH(f)p FJ(x)2578 4338 y FG(1)2617 4324 y FJ(;)d FI(\026)-52 b FJ(x)2709 4338 y FG(3)2749 4324 y FJ(;)15 b(x)2841 4338 y FG(4)2881 4324 y FH(g)23 b FK(is)f(a)h(clause.)30 b(A)22 b(clause)i FJ(C)k FK(is)83 4436 y FF(satis\002ed)i FK(by)25 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b(then,)83 1509 y(we)26 b(\002nd)h(another)h(problem)g FI(\005)1078 1476 y FP(0)1128 1509 y FK(which)f(has)g(been)h(sho)n(wn)f (to)g(be)g Fo(NP)p FK(-complete,)i(and)e(sho)n(w)g(that)h FI(\005)3361 1476 y FP(0)3415 1509 y FH(\024)3486 1523 y FC(p)3557 1509 y FI(\005)p FK(.)38 b(Note)83 1622 y(the)22 b(direction)j(of)c(reduction)k(here.)k(Man)o(y)22 b(students)i(ha)n(v)o (e)e(done)h(the)f(reduction)j(in)d(the)g(wrong)g(direction,)j(due)d(to) g(the)83 1735 y(some)n(what)i(confusing)i(nature)f(of)f(the)g(w)o(ord)f (\223reducible\224)k(in)c(this)h(conte)o(xt.)224 1848 y(Another)32 b(point)f(w)o(orth)g(noticing)h(is)f(that)f(\002nding)i(a) e(reduction)i(often)g(helps)f(us)g(understand)i(the)e(structure)h(of)83 1961 y(the)24 b(problem)g(at)f(hand)i(much)e(better)-5 b(.)30 b(In)23 b(ef)n(fect,)h(we)f(sho)n(w)g(that)h(our)g(problem)g(is) f(a)g(special)i(case)f(of)g(another)h(kno)n(wn)83 2074 y(problem.)31 b(If)23 b(there)i(w)o(as)e(a)h(good)h(approximation)i 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FH(C)k FK(is)c(satis\002able)h(if)n(f)e FJ(G)h FK(is)f FI(3)p FK(-colorable.)224 4026 y(The)j(main)g(idea)h(is)f(that,)i(for)e (each)h(triangle)h FJ(C)1738 4040 y FC(j)1775 4026 y FK(,)e(if)g(the)g(tree)h(e)o(xtra)g(v)o(ertices)h(get)e(the)h(same)f (color)h(then)g(there)g(is)83 4139 y(no)j(w)o(ay)g(to)g(color)h(the)g (inner)g(three)g(v)o(ertices)h(with)e(three)h(colors.)50 b(On)29 b(the)i(other)g(hand,)h(if)e(there)h(are)g(at)f(least)h(tw)o(o) 83 4252 y(outside)25 b(colors,)g(then)f(the)g(inner)h(v)o(ertices)g (can)f(al)o(w)o(ays)g(be)g(colored.)224 4365 y(Suppose)33 b(\002rst)e(that)h FH(C)k FK(is)31 b(satis\002able)i(with)f(truth)g (assignment)i FJ(t)p FK(.)51 b(Color)32 b(the)g(top)g(v)o(erte)o(x)g FJ(v)i FK(with)d(color)h FI(1)p FK(.)52 b(If)83 4478 y FJ(t)p FI(\()p FJ(x)203 4492 y FC(i)231 4478 y FI(\))35 b(=)h FE(T)t(R)q(U)t(E)c FK(then)d(color)h FJ(a)1086 4492 y FC(x)1126 4502 y Fs(i)1184 4478 y FK(and)f FJ(c)1382 4492 y FC(x)1422 4502 y Fs(i)1480 4478 y FK(with)f FI(2)p 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b(is)g(easy)h(to)f(check)h(that)g(this)g(assignment)83 5381 y(satis\002es)d(all)e(of)g(the)h(clauses.)29 b(Consider)22 b(a)e(clause)i FJ(C)1759 5395 y FC(j)1796 5381 y FK(,)e(for)g (instance.)30 b(If)20 b FJ(C)2457 5395 y FC(j)2513 5381 y FK(is)g(not)h(satis\002able)h(then)g(all)e(three)h(outside)1928 5782 y(17)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 83 91 a FK(v)o(ertices)27 b(of)e(its)h (triangle)h(must)f(ha)n(v)o(e)g(the)f(same)h(color)g(as)g(the)f(top)h (v)o(erte)o(x,)g(which)g(means)g(the)g(inner)g(v)o(ertices)h(of)f FJ(C)3827 105 y FC(j)83 204 y FK(were)d(not)h(properly)i(colored.)p 3797 317 4 62 v 3801 259 55 4 v 3801 317 V 3855 317 4 62 v 83 606 a FM(6)119 b(Exer)n(cises)83 813 y Ft(Exer)n(cise)25 b(1.)42 b FK(Sho)n(w)23 b(that)j(S)t FE(E)t(T)i FK(C)t FE(OV)t(E)t(R)e FK(is)e Fo(NP)p FK(-complete.)83 985 y Ft(Exer)n(cise)h(2.)42 b FK(Sho)n(w)23 b(that)j(D)t FE(O)t(M)t(I)t(N)r(A)l(T)t(I)t(N)t(G)j FK(S)t FE(E)t(T)d FK(is)e Fo(NP)p FK(-complete.)83 1156 y Ft(Exer)n(cise)h(3.)42 b FK(Sho)n(w)23 b(that)j(K)t FE(N)r(A)t(P)t(S)t(A)q(C)t(K)g FK(is)d Fo(NP)q FK(-complete.)83 1327 y Ft(Exer)n(cise)i(4.)42 b FK(Sho)n(w)23 b(that)h(TSP)d(is)i Fo(NP)q FK(-complete.)83 1498 y Ft(Exer)n(cise)i(5.)42 b FK(Sho)n(w)23 b(that)h FJ(k)5 b FK(-)t FE(C)t(O)t(L)t(O)t(R)t(A)t(B)t(I)t(L)t(I)t(T)t(Y)30 b FK(is)23 b Fo(NP)p FK(-complete.)224 1669 y(F)o(or)36 b(the)h(follo)n(wing)h(e)o(x)o(ercises,)k(assume)37 b(that)h(you)f (only)h(kno)n(w)e(the)h(problems)i(in)d(our)h(roadmap)i(are)d Fo(NP)q FK(-)83 1782 y(complete.)83 1953 y Ft(Exer)n(cise)25 b(6.)42 b FK(Gi)n(v)o(e)23 b(a)g(polynomial)j(time)d(reduction)j(from)e FI(3)p FK(-SA)-10 b(T)22 b(to)j(C)t FE(L)t(I)t(Q)s(U)t(E)r FK(.)83 2124 y Ft(Exer)n(cise)g(7)e FK(\(**\))p Ft(.)43 b FK(Gi)n(v)o(e)23 b(a)g(polynomial)j(time)d(reduction)j(from)g(H)t FE(A)t(M)t(I)t(L)m(T)s(O)t(N)t(I)t(A)t(N)k FK(C)t FE(Y)t(C)t(L)t(E)d FK(to)e(V)t FE(E)t(RT)t(E)t(X)30 b FK(C)t FE(OV)t(E)t(R)r FK(.)83 2295 y Ft(Exer)n(cise)24 b(8)d FK(\(*\))p Ft(.)40 b FK(A)21 b FF(monotone)j(boolean)g(formula)f FK(is)f(a)f(boolean)j (formula)f(which)f(in)l(v)n(olv)o(es)j(only)f FE(A)t(N)t(D)r FK(')-5 b(s)22 b(and)j FE(O)t(R)r FK(')-5 b(s.)83 2408 y(There)33 b(is)f(no)h(ne)o(gation.)57 b(F)o(or)32 b(instance,)k FJ(\036)42 b FI(=)g(\()p FJ(x)1738 2422 y FG(1)1804 2408 y FH(^)27 b FJ(x)1944 2422 y FG(2)1983 2408 y FI(\))g FH(_)g FI(\()p FJ(x)2220 2422 y FG(3)2287 2408 y FH(_)f FI(\()p FJ(x)2461 2422 y FG(4)2528 2408 y FH(^)g FJ(x)2667 2422 y FG(5)2706 2408 y FI(\)\))33 b FK(is)f(monotone.)58 b(Pro)o(v)o(e)32 b(that)h(the)83 2521 y(follo)n(wing)25 b(problem)g(is)e Fo(NP)p FK(-complete.)85 2692 y(M)t FE(O)t(N)t(O)q(T)s(O)t(N)t(E)29 b FK(S)t FE(A)l(T)t(I)t(S)t(FI)t(A)t(B) t(I)t(L)t(I)t(T)5 b(Y)30 b FK(\()r(M)t FE(O)t(N)t FK(-)t(S)t(A)-6 b(T)r(\))312 2804 y FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)56 b(A)34 b(set)i FJ(X)42 b FK(of)35 b(v)n(ariables,)40 b(a)35 b(monotone)i(boolean)h(formula)e FJ(\036)f FK(o)o(v)o(er)g FJ(X)7 b FK(,)38 b(and)e(a)e(bound)310 2917 y FJ(b)26 b FH(2)e FB(Z)521 2884 y FG(+)580 2917 y FK(.)312 3064 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)46 b(Is)31 b(there)g(a)f(truth)h(assignment)i(which)e(satis\002es)h FJ(\036)d FK(in)i(which)g(at)f(most)g FJ(b)g FK(v)n(ariables)j(are)312 3177 y FE(T)t(R)q(U)t(E)t FK(?)83 3348 y Ft(Exer)n(cise)25 b(9.)42 b FK(Pro)o(v)o(e)23 b(that)h(the)g(follo)n(wing)h(problem)g(is) e Fo(NP)p FK(-complete.)85 3519 y(L)t FE(O)t(N)t(G)t(E)t(S)t(T)30 b FK(P)m FE(A)l(T)t(H)312 3632 y(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)i(A)23 b(graph)i FJ(G)e FK(and)h(a)f(bound)i FJ(b)g FH(2)g FB(Z)1843 3599 y FG(+)1902 3632 y FK(.)312 3779 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)32 b(Is)24 b(there)g(a)f(path)i(in)e FJ(G)g FK(of)h(length)h(at)e(least)h FJ(b)p FK(?)83 3950 y Ft(Exer)n(cise)h(10.)42 b FK(Pro)o(v)o(e)24 b(that)g(the)f(follo)n(wing)i(problem)g(is)f Fo(NP)p FK(-complete.)85 4121 y(H)t FE(I)t(T)t(T)t(I)t(N)t(G)30 b FK(S)t FE(E)t(T)312 4234 y(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)i(A)22 b(collection)k FH(C)k FI(=)25 b FH(f)p FJ(S)1496 4248 y FG(1)1536 4234 y FJ(;)15 b(:)g(:)g(:)h(;)f(S)1793 4248 y FC(m)1860 4234 y FH(g)23 b FK(of)f(non-empty)j(subsets)g(of)e(a) f(uni)n(v)o(erse)j(set)e FJ(S)5 b FK(,)22 b(and)h(a)310 4347 y(bound)i FJ(b)h FH(2)e FB(Z)771 4314 y FG(+)830 4347 y FK(.)312 4494 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)48 b(Is)31 b(there)h(a)e(subset)j FJ(H)46 b FH(\022)39 b FJ(S)c FK(with)c FH(j)p FJ(H)7 b FH(j)40 b(\024)f FJ(h)p FK(,)32 b(for)g(which)f FJ(S)2764 4508 y FC(i)2818 4494 y FH(\\)25 b FJ(H)47 b FH(6)p FI(=)39 b FH(;)p FK(,)32 b(for)f(all)g FJ(i)40 b FI(=)310 4607 y(1)p FJ(;)15 b(:)g(:)g(:)i(;)e (m)p FK(?)83 4778 y Ft(Exer)n(cise)25 b(11.)42 b FK(Pro)o(v)o(e)24 b(that)g(the)f(follo)n(wing)i(problem)g(is)f Fo(NP)p FK(-complete.)85 4949 y(P)m FE(A)t(RT)t(I)t(T)t(I)t(O)t(N)312 5062 y(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)32 b(A)23 b(set)h FJ(A)h FI(=)g FH(f)p FJ(a)1247 5076 y FG(1)1287 5062 y FJ(;)15 b(:)g(:)g(:)i(;)e(a)1537 5076 y 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