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Every Polynomial-Time 1-Degree Collapses Iff P = Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer
Every Polynomial-Time 1-Degree Collapses Iff P = Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer
Electrical Engineering and Computer Science - All Scholarship
A set A is m-reducible (or Karp-reducible) to B iff there is a polynomial-time computable function f such that, for all x, x ∈ A <--> f (x) ∈ B. Two sets are: (a) 1-equivalent iff each is m-reducible to the other by one-one reductions; (b) p-invertible equivalent iff each is m-reducible to the other by one-one, polynomial-time invertible reductions; and (c) p-isomorphic iff there is an m-reduction from one set to the other that is one-one, onto, and polynomial-time invertible. In this paper we show the following characterization. Theorem : The following are equivalent: (a) P = PSPACE. (b) Every …