HW9Soln

HW9Soln - CSCI 2670 November 9, 2005 HW 9 5.7 If A is...

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CSCI 2670 November 9, 2005 HW 9 5.7 If A is Turing-recognizable and A m Ā, then (by Theorem 5.28) Ā is Turing- recognizable – i.e., A is co-Turing-recognizable. Therefore, (by Theorem 4.22) A is decidable since A is both Turing-recognizable and co-Turing-recognizable. 5.12 Assume it is decidable to determine if a single-tape Turing machine ever writes a blank symbol over a nonblank symbol during the course of its input string on any computation and assume that D decides this language. We want to use D to decide A TM . Given any <M,w>, we want to create a Turing machine that writes a blank over a nonblank if and only if M accepts w. We can create a new Turing machine M 1 that does the following: rejects every string other than w replaces all transitions that write a blank symbol with transitions that write an x, where x is some symbol not in the tape alphabet adds a new transition for every transition that reads a blank symbol – the new transition would do exactly the same thing as the original except it would read an x instead of a blank, where x is the same symbol used above
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HW9Soln - CSCI 2670 November 9, 2005 HW 9 5.7 If A is...

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