homework8

# homework8 - 5.3 ab abab ab abab aba b b a b a aa a aa a 5.9...

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5.3 ab ab aba b b aa aa abab abab b a a a a 5.9: Let T = { <M> | M is a TM that accepts w r whenever it accepts w }. Assume T is decidable and let decider R decide T. Reduce from Atm by constructing a TM S as follows: S: on input <M,w> 1. create a TM Q as follows: On input x: 1. if x does not have the form 01 or 10 reject. 2. if x has the form 01, then accept. 3. else (x has the form 10), Run M on w and accept if M accepts w. 2. Run R on <Q> 3. Accept if R accepts, reject if R rejects. Because S decides Atm, which is known to be undecidable, we then know that T is not decidable. 5.12: Let L = { <M> | M is a TM and M writes a blank symbol over a nonblank symbol during the course of it’s computation on any string } Assume L is decidable and R be a decider for L. Reduce from Atm by constructing a TM S as follows: S: on input <M,w> 1. create a TM Q based on M as follows: On input w: 1. Replace all transitions in M that read or write a blank symbol to read or write a new tape symbol # 2. Replace each accept transition with three operations to write a nonblank symbol, move the head back to this position, write a

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## This note was uploaded on 04/10/2008 for the course CSE 105 taught by Professor Paturi during the Fall '99 term at UCSD.

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homework8 - 5.3 ab abab ab abab aba b b a b a aa a aa a 5.9...

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