### Abstract

Summary form only given. It is proved that if P ≠ NP, then there exits a set in NP that is polynomial-time bounded truth-table reducible to no sparse set. By using the technique proving this result, intractability of several number theoretic decision problems, i.e., decision problems defined naturally from number theoretic problems, is investigated. It is shown that for those number theoretic decision problems, if it is not in P, then it is polynomial-time bounded truth-table reducible to no sparse set.

Original language | English (US) |
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Title of host publication | Proc Fifth Annu Struct Complexity Theor |

Publisher | Publ by IEEE |

Number of pages | 1 |

ISBN (Print) | 0818620722 |

State | Published - Dec 1 1990 |

Externally published | Yes |

Event | Proceedings of the Fifth Annual Structure in Complexity Theory Conference - Barcelona, Spain Duration: Jul 8 1990 → Jul 11 1990 |

### Publication series

Name | Proc Fifth Annu Struct Complexity Theor |
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### Other

Other | Proceedings of the Fifth Annual Structure in Complexity Theory Conference |
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City | Barcelona, Spain |

Period | 7/8/90 → 7/11/90 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

Ogiwara, M., & Watanabe, O. (1990). On polynomial time bounded truth-table reducibility of NP sets to sparse sets. In

*Proc Fifth Annu Struct Complexity Theor*(Proc Fifth Annu Struct Complexity Theor). Publ by IEEE.