Complexity Theory - Tutorial

It is clear that Ñ would accept L (N accepts if one branch ends up in the accepting state. Ñ would notice that as rejecting state it would reject as soon as there is one rejecting state because all the states are universal. N rejects if no branch end in an accepting state, i.e., all end up in the rejecting state. But for Ñ that would mean that all the branches are accepting, therefore, it would accept.) Also, since the computation is exactly the same, it is also clear that it is poly-time Turing machine. The second way of solving this problem is by recalling that TAUTOLOGY is coNP complete problem. This means that any instance of problem in coNP can be reduced by a polynomial deterministic Turing machine to an instance of TAUTOLOGY. But for TAUTOLOGY we’ve already proven that it is in AP.