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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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 Fall '99
 Paturi

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