### Abstract

Hartmanis conjectured that there exist no sparse complete sets for P under logspace many-one reductions. In this paper, in support of the conjecture, it is shown that if P has sparse hard sets under logspace many-one reductions, then P is contained as a subset within DSPACE[log^{2} n]. The result follows from a more general statement: if P has 2^{polylog} sparse hard sets under poly-logarithmic space-computable many-one reductions, then P is contained as a subset within DSPACE[polylog].

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundations of Computer Science - Proceedings |

Editors | Anon |

Publisher | IEEE |

Pages | 354-361 |

Number of pages | 8 |

State | Published - 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science - Milwaukee, WI, USA Duration: Oct 23 1995 → Oct 25 1995 |

### Other

Other | Proceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science |
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City | Milwaukee, WI, USA |

Period | 10/23/95 → 10/25/95 |

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science - Proceedings*(pp. 354-361). IEEE.

**Sparse P-hard sets yield space-efficient algorithms.** / Ogihara, Mitsunori.

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

*Annual Symposium on Foundations of Computer Science - Proceedings.*IEEE, pp. 354-361, Proceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science, Milwaukee, WI, USA, 10/23/95.

}

TY - GEN

T1 - Sparse P-hard sets yield space-efficient algorithms

AU - Ogihara, Mitsunori

PY - 1995

Y1 - 1995

N2 - Hartmanis conjectured that there exist no sparse complete sets for P under logspace many-one reductions. In this paper, in support of the conjecture, it is shown that if P has sparse hard sets under logspace many-one reductions, then P is contained as a subset within DSPACE[log2 n]. The result follows from a more general statement: if P has 2polylog sparse hard sets under poly-logarithmic space-computable many-one reductions, then P is contained as a subset within DSPACE[polylog].

AB - Hartmanis conjectured that there exist no sparse complete sets for P under logspace many-one reductions. In this paper, in support of the conjecture, it is shown that if P has sparse hard sets under logspace many-one reductions, then P is contained as a subset within DSPACE[log2 n]. The result follows from a more general statement: if P has 2polylog sparse hard sets under poly-logarithmic space-computable many-one reductions, then P is contained as a subset within DSPACE[polylog].

UR - http://www.scopus.com/inward/record.url?scp=0029489415&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029489415&partnerID=8YFLogxK

M3 - Conference contribution

SP - 354

EP - 361

BT - Annual Symposium on Foundations of Computer Science - Proceedings

A2 - Anon, null

PB - IEEE

ER -