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If it was verifiable in NP time, and P = NP, then wouldn't it also be verifiable in polynomial time?


Is that correct? I'm not sure. NP problems are verifiable in deterministic polynomial time. That includes the hardest of NP problems (NP-complete problems, e.g. travelling salesman and graph coloring). Are there problems that are "harder" than that? I never learned about anything outside NP—I know there are other complexity classes out there (like probabilistic classes), but I don't know how they compare to NP. My guess is that anything outside NP is essentially a non-deterministic problem altogether, meaning the "answer" isn't formally a simple "yes" or "no."


but wouldn't it be just plain NP then




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