### Abstract

The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact it is proved that, for any class K chosen from a certain set of complexity classes, it holds that (1) if there is a sparse polynomial-time bounded-truth-table-hard set for K, then K = P, and (2) if there is a sparse strongly nondeterministic bounded-truth-table-hard set for K, then K ⊂ NP 23 co-NP. The main result also shows that the same facts hold for the class PSPACE.

Original language | English (US) |
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Title of host publication | Proc 6 Annu Struct Complexity Theor |

Publisher | Publ by IEEE |

Pages | 139-151 |

Number of pages | 13 |

ISBN (Print) | 0818622555 |

State | Published - 1991 |

Externally published | Yes |

Event | Proceedings of the 6th Annual Structure in Complexity Theory Conference - Chicago, IL, USA Duration: Jun 30 1991 → Jul 3 1991 |

### Other

Other | Proceedings of the 6th Annual Structure in Complexity Theory Conference |
---|---|

City | Chicago, IL, USA |

Period | 6/30/91 → 7/3/91 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc 6 Annu Struct Complexity Theor*(pp. 139-151). Publ by IEEE.

**On one query, self-reducible sets.** / Ogihara, Mitsunori; Lozano, Antoni.

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

*Proc 6 Annu Struct Complexity Theor.*Publ by IEEE, pp. 139-151, Proceedings of the 6th Annual Structure in Complexity Theory Conference, Chicago, IL, USA, 6/30/91.

}

TY - GEN

T1 - On one query, self-reducible sets

AU - Ogihara, Mitsunori

AU - Lozano, Antoni

PY - 1991

Y1 - 1991

N2 - The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact it is proved that, for any class K chosen from a certain set of complexity classes, it holds that (1) if there is a sparse polynomial-time bounded-truth-table-hard set for K, then K = P, and (2) if there is a sparse strongly nondeterministic bounded-truth-table-hard set for K, then K ⊂ NP 23 co-NP. The main result also shows that the same facts hold for the class PSPACE.

AB - The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact it is proved that, for any class K chosen from a certain set of complexity classes, it holds that (1) if there is a sparse polynomial-time bounded-truth-table-hard set for K, then K = P, and (2) if there is a sparse strongly nondeterministic bounded-truth-table-hard set for K, then K ⊂ NP 23 co-NP. The main result also shows that the same facts hold for the class PSPACE.

UR - http://www.scopus.com/inward/record.url?scp=0026398367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026398367&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0818622555

SP - 139

EP - 151

BT - Proc 6 Annu Struct Complexity Theor

PB - Publ by IEEE

ER -