### 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 language | English (US) |
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Pages (from-to) | 713-741 |

Number of pages | 29 |

Journal | Journal of Symbolic Logic |

Volume | 69 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2004 |

### ASJC Scopus subject areas

- Philosophy
- Logic

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## Cite this

*Journal of Symbolic Logic*,

*69*(3), 713-741. https://doi.org/10.2178/jsl/1096901763