A Negative Answer to P?=PSPACE

06/22/2021

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by   Tianrong Lin, et al.

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There is a conjecture on P?=PSPACE in computational complexity zoo. It is a widespread belief that P≠ PSPACE, otherwise P=NP which is extremely impossible. In this short work, we assert that P≠ PSPACE no matter what outcome is on P?=NP. We accomplishe this via showing NP≠ PSPACE. The method is by the result that Circuit-SAT is ≤_log–complete for NP, Circuit-SAT∈ DSPACE[n], the known result DSPACE[n^1+c]⊂ DSPACE[n^2(1+c)] (indicated by the space complexity hierarchy theorem) and the fact that PSPACE is the union set of all DSPACE[n^k] where k∈ℕ. Closely related consequences are summarized.