I could not understand, why is the following proof of L being in NP and coNP fails:
We make a verifier that gets M, x, k, and a list of configurations which led to the acceptance/rejection of x.
It verifies that the configurations are valid for M and follow each other, that the last one is in accept/reject state… etc. it seems polynomial in the size of input.
And the same with the complement of L (which says, M does not stop within k steps): with a list of configurations of length k which does not lead to accept/reject state. Thus showing that M did not stop in k steps.
And so, L and its complement are in NP.
But what's wrong here?
Thanks in advance.