Abstract

A set A is m-reducible to B if and only if there is a polynomial-time computable function f such that, for all x, x∈ A if and only if f ∈ B. Two sets are: 1-equivalent if and only if each is m-reducible to the other by one-one reductions; p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and p-isomorphic if and only if 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: P = PSPACE. Every two 1-equivalent sets are p-isomorphic. Every two p-invertible equivalent sets are p-isomorphic.