### Abstract

We distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. Results include: (i) If NE ≠ E, then there exists a set t in NP - P such that search reduces to decision for L, search does not nonadaptively reduce to decision for L and L is not self-reducible, (ii) If UE ≠ E, then there exists a language L ∈ UP - P such that search nonadaptively reduces to decision for L, but L is not self-reducible, (iii) If UE ∩ co-UE ≠ E, then there is a disjunctive self-reducible language L ∈ UP - P for which search does not nonadaptively reduce to decision. We prove that if NE ⊈ BPE, then there is a language L ∈ NP - BPP such that L is randomly self-reducible, not nonadaptively randomly self-reducible, and not self-reducible. We obtain results concerning trade-offs in multiprover interactive proof systems and results that distinguish checkable languages from those that are nonadaptively checkable. Many of our results are proven by constructing p-selective sets. We obtain a p-selective set that is not ≤ ^{P}_{tt}-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ ^{P}_{T}-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ ^{P}_{m}-equivalent to a tally language. We construct a recursive p-selective tally set that is not cheatable.

Original language | English (US) |
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Pages (from-to) | 194-209 |

Number of pages | 16 |

Journal | Journal of Computer and System Sciences |

Volume | 53 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1996 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computer and System Sciences*,

*53*(2), 194-209. https://doi.org/10.1006/jcss.1996.0061