### Abstract

It is proved that if P ≠ NP, then there exists a set in NP that is not polynomial-time bounded truth-table reducible (in short, ≤_{btt}^{P}-reducible) to any sparse set. In other words, it is proved that no sparse ≤_{btt}^{P}-hard set exists for NP unless P = NP. By using the technique proving this result, the intractability of several number-theoretic decision problems, i.e., decision problems defined naturally from number-theoretic problems is investigated. It is shown that for these number-theoretic decision problems, if it is not in P, then it is not ≤_{btt}^{P}-reducible to any sparse set.

Original language | English (US) |
---|---|

Pages (from-to) | 471-483 |

Number of pages | 13 |

Journal | SIAM Journal on Computing |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1991 |

Externally published | Yes |

### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)

## Fingerprint Dive into the research topics of 'On polynomial-time bounded truth-table reducibility of NP sets to sparse sets'. Together they form a unique fingerprint.

## Cite this

Ogiwara, M., & Watanabe, O. (1991). On polynomial-time bounded truth-table reducibility of NP sets to sparse sets.

*SIAM Journal on Computing*,*20*(3), 471-483. https://doi.org/10.1137/0220030