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CSCI 2670
November 9, 2005
HW 9
5.7
If A is Turingrecognizable and A
≤
m
Ā, then (by Theorem 5.28) Ā is Turing
recognizable – i.e., A is coTuringrecognizable.
Therefore, (by Theorem 4.22) A is
decidable since A is both Turingrecognizable and coTuringrecognizable.
5.12
Assume it is decidable to determine if a singletape 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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 Spring '11
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