### 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 - Dec 1 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 |

### Publication series

Name | Proc 6 Annu Struct Complexity Theor |
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### Other

Other | Proceedings of the 6th Annual Structure in Complexity Theory Conference |
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City | Chicago, IL, USA |

Period | 6/30/91 → 7/3/91 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

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