October 5

# October 5 - construction October 5 2005 6 Equivalent...

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CSCI 2670 Introduction to Theory of Computing October 5, 2005

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October 5, 2005 2 Quiz (6 points) Describe a Turing machine that accepts the following language {a n b m | n > 0 and m = n – 1} (4 points) Demonstrate how your Turing machine would calculate the string aaabb
October 5, 2005 3 Variants of Turing machines Robustness of model Varying the model does not change the power Example, making finite automata nondeterministic Simple variant of TM model Add “stay put” direction Other variants More tapes Nondeterministic

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October 5, 2005 4 Multitape Turing machines Same as standard Turing machine, but have several tapes TM definition changes only in definition of δ δ : Q × Г k Q × Г k × {L,R} k
October 5, 2005 5 Equivalence of machines Theorem: Every multitape Turing machine has an equivalent single tape Turing machine Proof method:

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Unformatted text preview: construction October 5, 2005 6 Equivalent machines M 0 1 ~ ~ ~ ~ ~ ~ a a a ~ ~ ~ ~ ~ a b ~ ~ ~ ~ ~ ~ # 1 # a a a # a b # ~ ~ S October 5, 2005 7 Simulating k-tape behavior • Single tape start string is #w#~ #...#~ # • Each move proceeds as follows: – Start at leftmost slot – Scan right to (k+1) st # to find symbol at each virtual tape head – Make second pass making updates indicated by k-tape transition function – When a virtual head moves onto a #, shift string to right October 5, 2005 8 Corollary Corollary: A language is Turing-recognizable if and only if some multitape Turing machine recognizes it. October 5, 2005 9 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 5 - construction October 5 2005 6 Equivalent...

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