### 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 |

Pages | 2 |

Number of pages | 1 |

ISBN (Print) | 0818620722 |

State | Published - 1990 |

Externally published | Yes |

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

### Other

Other | Proceedings of the Fifth Annual Structure in Complexity Theory Conference |
---|---|

City | Barcelona, Spain |

Period | 7/8/90 → 7/11/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc Fifth Annu Struct Complexity Theor*(pp. 2). Publ by IEEE.

**On polynomial time bounded truth-table reducibility of NP sets to sparse sets.** / Ogihara, Mitsunori; Watanabe, Osamu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proc Fifth Annu Struct Complexity Theor.*Publ by IEEE, pp. 2, Proceedings of the Fifth Annual Structure in Complexity Theory Conference, Barcelona, Spain, 7/8/90.

}

TY - GEN

T1 - On polynomial time bounded truth-table reducibility of NP sets to sparse sets

AU - Ogihara, Mitsunori

AU - Watanabe, Osamu

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025599316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025599316&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0818620722

SP - 2

BT - Proc Fifth Annu Struct Complexity Theor

PB - Publ by IEEE

ER -