常见问题讨论中kleene star路径挑战1 problem session 2会话.pptx

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常见问题讨论中kleene star路径挑战1 problem session 2会话.pptx

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1DiscussionofCommonProblems–2KleeneStarPathsinDFAChallengeProblem1

KleeneStarExample1*DoesNOTmeananinfinitelongstringof1’sL(1*)={ε,1,11,111,1111,…}EachelementinL(1*)hasfinitelength2

InfinitenessInfiniteobjectsareimportantin

mathematics(setofintegers,alinecontaininginfinitenumberofpoints)Inacomputationalmodel,youcanneverreadsuchobjectintoacomputerUnlessyoucanrepresentitinfiniteformRegularexpressionforaregularlanguageTriple(a,b,c)foralineax+by+c=03

Whatis“Last”ADFAwhichacceptsallstringsof0’sand1’sexceptthosewhoselastcharacteris1Whataboutthestring1?Thelastcharacterofanystringa1a2…anisjustan(n1).So1isnotacceptedbythisDFAεhasno“last”character,soitISacceptedbythisDFA4

ConvertDFAintoREReviewk-PathInductionLetRijkbetheregularexpressionforthesetoflabelsofk-pathsfromstateitoj5

66k-PathInductiveCaseAk-pathfromitojeither:Nevergoesthroughstatek,orGoesthroughkoneormoretimes.Rijk=Rijk-1+Rikk-1(Rkkk-1)*Rkjk-1.Doesn’tgothroughkGoesfromitokthefirsttimeZeroormoretimesfromktokThen,fromktoj

ZoominWhatisRikk-1(Rkkk-1)*Rkjk-1?…Rkkk(Rkkk-1)*=Rkkk7ikkkjkkkkk

ChallengeProblem1Lisalanguagewithalphabet{0,1,2}Lcontainsnostringsthathaveanythreeconsecutive0s,anythreeconsecutive1s,oranythreeconsecutive2s.e.g.isnotinLProvethatLisregularandgiveaDFAforL.8

ChallengeProblem1ThecomplementofLhasaregularexpression:(0+1+2)*(000+111+222)(0+1+2)*AllstringsthatDOcontainthreeconsecutive0sor1sor2s.?Regularlanguagesareclosedundercomplement9

ChallengeProblem1DFAforLThestaterepresentstherunofthesamesymbolthatappearsattheendofthestringStartstateSStatea0,a00,a1,a11,a2,a22DeadstateDExample:012011shouldgettoa1110

ChallengeProblem1012?*Sa0a1a2*a0a00a1a2*a1a0