Every polynomial-time 1-degree collapses if and only if P = PSPACE

Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Research output: Contribution to journalArticle

Abstract

A set A is m-reducible (or Karp-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 (x) ∈ 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: (a) P = PSPACE. (b) Every two 1-equivalent sets are p-isomorphic. (c) Every two p-invertible equivalent sets are p-isomorphic.

Original languageEnglish (US)
Pages (from-to)713-741
Number of pages29
JournalJournal of Symbolic Logic
Volume69
Issue number3
DOIs
StatePublished - Sep 2004

ASJC Scopus subject areas

  • Philosophy
  • Logic

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