Is the following language decidable?
L = {(M) : M performs at least 100 steps on every accepted input.}
I tried to use reduction from the halting problem, but still no dice.
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1$\begingroup$ Cross-posted: cs.stackexchange.com/q/70747/755, stackoverflow.com/q/42428695/781723. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. $\endgroup$– D.W. ♦Feb 24 '17 at 19:23
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Yes, it is decidable. There is a limited amount of input that any Turing machine could look at in ≤ 100 steps, so you can test a simulation of any given machine $M$ against all of those possibilities.
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2$\begingroup$ Next time, consider waiting until the OP reveals what effort, if any, they expended on solving the problem themselves. $\endgroup$ Feb 24 '17 at 3:17