### Abstract

This paper introduces and studies a notion called polynomial-time membership comparable sets, which is a generalization of P-selective sets. For a function g, a set A is called polynomial-time g-membership comparable if there is a polynomial-time computable function f such that for any x_{1},···,x_{m} with m≥g(max{|x_{1}|, ···,|x_{m}|}), outputs bqq{0,1}^{m} such that (A(x_{1}),···, A(x_{m}))≠b. It is shown for each C chosen from {PSPACE,UP,FewP,NP,C_{=}PP,MOD_{2}P,MOD_{3}P,· ··}, that if all of C are polynomial-time c(log n)-membership comparable for some fixed constant c<1, then C = P. As a corollary, it is shown that if there is some constant c<1 such that all of C are polynomial-time n^{c}-truth-table reducible to some P-selective sets, then C = P, which resolves a question that has been left open for a long time.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Annual Structure in Complexity Theory Conference |

Editors | Anon |

Publisher | Publ by IEEE |

Pages | 2-11 |

Number of pages | 10 |

ISBN (Print) | 0818656727 |

State | Published - Dec 1 1994 |

Externally published | Yes |

Event | Proceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth Duration: Jun 28 1994 → Jul 1 1994 |

### Publication series

Name | Proceedings of the IEEE Annual Structure in Complexity Theory Conference |
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ISSN (Print) | 1063-6870 |

### Other

Other | Proceedings of the 9th Annual Structure in Complexity Theory Conference |
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City | Amsterdam, Neth |

Period | 6/28/94 → 7/1/94 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Proceedings of the IEEE Annual Structure in Complexity Theory Conference*(pp. 2-11). (Proceedings of the IEEE Annual Structure in Complexity Theory Conference). Publ by IEEE.