October 6

October 6 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing October 6, 2005
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October 6, 2005 2 Agenda •Yester day – Variants of Turing machines • Allow “stay put” state • Multiple tapes •Today – Quick revisit of multiple tapes – Non-determinism • Prove equivalence of deterministic and nondeterministic Turing machines – Enumerators • Prove equivalence of enumerators and
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October 6, 2005 3 Announcements • Homework due next Tuesday • 3.7 and 3.15 are same in both texts • 3.16 d – Show the collection of Turing- recognizable languages is closed under the operation of intersection.
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October 6, 2005 4 Corollary Corollary: A language is Turing- recognizable if and only if some multitape Turing machine recognizes it.
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October 6, 2005 5 Example • Using 2-tape Turing machine, write a copy machine • Copy tape 1 to tape 2 • Move tape 1 to beginning • Copy tape 1 to tape 2 • Accept
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October 6, 2005 6 Copy machine {a,~} {x,a},{R,R} {b,~} {y,b},{R,R} {~,~} {L,L} q accept ~,~ {L,S} {x,~} {a,a},{R,R} {y,~} {b,b},{R,R} {~ ,~} {R,R} q reject {a,~} {a,a},{R,R} {b,~} {b,b},{R,R} {a,~} {L,S} {b,~} {L,S} {a,~} {a,a},{R,R} {b,~} {b,b},{R,R}
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October 6, 2005 7 Copy machine a x,R
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October 6 - CSCI 2670 Introduction to Theory of Computing...

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