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I understand this is a slightly vague question, but there are results for P vs.

ID: 652221 • Letter: I

Question

I understand this is a slightly vague question, but there are results for P vs. NP, such as the question cannot be easily resolved using oracles. Are there any results like this which have been shown for P vs. NP but have not been shown for P vs PSPACE, so that there is hope that certain proof techniques might resolve P vs PSPACE even though they cannot resolve P vs NP? And are there any non-trivial results that say that if P = PSPACE then there are implications that do not necessarily hold under P = NP? Or anything else non-trivial in the literature that suggests it's easier to prove P != PSPACE than it is to prove P != NP?

Explanation / Answer

This doesn't really answer your question, but there is a result that under a restricted form of time travel (yes, time travel), it holds that P=PSPACE. I'll remark that the result is nontrivial, given the restrictions on the model. See this explanation by Scott Aaronson.