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Douglas_Knight comments on The Curve of Capability - Less Wrong
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I'm confused or about to display my ignorance. When you write:
Are you saying that evaluating a Go position has exponential (time?) cost even on a nondeterministic machine? I thought that any given string of moves to the end of the game could be evaluated in polynomial (N^2?) time. I thought that the full set of possible strings of moves could be evaluated (naively) in exponential time on a deterministic machine and polynomial time on a nondeterministic machine - so I thought Go position evaluation would be in NP. I think you are saying that it is more costly than that. Are you saying that, and what am I getting wrong?
If one assumes everything that is conjectured, then yes. To say that it is EXP-hard is to say that it takes exponential time on a deterministic machine. This does not immediately say how much time it takes on a non-deterministic machine. It is not ruled out that NP=EXP, but it is extremely implausible. Also doubted, though more plausible, is that PSPACE=EXP. PSPACE doesn't care about determinism.