### Abstract

In this paper we give several generalized theorems concerning reducibility notions to certain complexity classes. We study classes that are either (I) closed under NP many-one reductions and polynomial-time conjunctive reductions or (II) closed under coNP many-one reductions and polynomial-time disjunctive reductions. We prove that, for such a class K, (1) reducibility notions of sets to K under polynomial-time constant-round truth-table reducibility, polynomial-time log-Turing reducibility, logspace constant-round truth-table reducibility, logspace log-Turing reducibility, and logspace Turing reducibility are all equivalent and (2) every set that is polynomial-time positive Turing reducible to a set in K is already in K. From these results, we derive some observations on the reducibility notions to C_{=}P and NP.

Original language | English (US) |
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Pages (from-to) | 189-200 |

Number of pages | 12 |

Journal | Mathematical systems theory |

Volume | 27 |

Issue number | 3 |

DOIs | |

State | Published - May 1 1994 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Mathematics(all)
- Computational Theory and Mathematics