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.


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.

  • 2
    $\begingroup$ Next time, consider waiting until the OP reveals what effort, if any, they expended on solving the problem themselves. $\endgroup$ – Yuval Filmus Feb 24 '17 at 3:17

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