COMP481 Review Problems Turing Machines and (Un ...

COMP481 ReviewProblemsTuringMachinesand(Un) ,I regularlymake useoftwo Problems ,namely TheHaltingProblem,denotedbyHP, andde nedasHP=fhM; wijMis a TMandit haltsonstringwg. ThecomplementoftheHaltingProblem,denoted byHP, andde nedasHP=fhM; wijMis a TMandit use decidable and recursive interchangeably, anduse semi-decidable and recursivelyenu-merable interchangeably. I useR forrecursive, : m denotesmappingreducibility. Forexample,L1 mL2means L1mappingreducestoL2 . show a languageLis notinR (notinRE),it suf cestoshow thatL0 mLforsomeL0thatis notinR (notinRE).Fromthetheoremwe've learned,it followsthatLis notinR (notinRE). mLis equivalenttoshowingL0 's Theorem(theversionI use): LetCbea proper, ,thelanguageLC=fhMi:L(M)2 Cgis notrecursive. So,toshowa languageLis notrecursive usingRice's Theorem,I picktheappropriateC( ,aCsuchthatLC=L), prove that(1)C RE, (2)C6=RE, and(3)C6=.

1. For each of the following languages, state whether each language is (I) recursive, (II) recursively enumerable but not recursive, or (III) not recursively enumerable. Prove your answer. † L1 = fhMijM is a TM and there exists an input on which M halts in less than jhMij stepsg. – R. M⁄ that decides the languages works as follows on ...

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  Review, Machine, Problem, Truing, Recursively enumerable, Recursively, Enumerable, Comp481 review problems turing machines and, Comp481

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