### Abstract

This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomial-time reducibilities, it is shown that 1. A multivalued partial function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable via 2^{k}-1 nonadaptive queries to NPMV. 2. A characteristic function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable with k adaptive queries to NP. 3. Unless the Boolean hierarchy collapses, k adaptive (nonadaptive) queries to NPMV is different than k+1 adaptive (nonadaptive) queries to NPMV for every k. Nondeterministic reducibilities, lowness and the difference hierarchy over NPMV are also studied. The difference hierarchy for partial functions does not collapse unless the Boolean hierarchy collapses, but, surprisingly, the levels of the difference and bounded query hierarchies do not interleave (as is the case for sets) unless the polynomial hierarchy collapses.

Original language | English (US) |
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Title of host publication | STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings |

Publisher | Springer Verlag |

Pages | 399-407 |

Number of pages | 9 |

Volume | 665 LNCS |

ISBN (Print) | 9783540565031 |

State | Published - 1993 |

Externally published | Yes |

Event | 10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993 - Wurzburg, Germany Duration: Feb 25 1993 → Feb 27 1993 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 665 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993 |
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Country | Germany |

City | Wurzburg |

Period | 2/25/93 → 2/27/93 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings*(Vol. 665 LNCS, pp. 399-407). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 665 LNCS). Springer Verlag.

**On using oracles that compute values.** / Fenner, Stephen; Homer, Steve; Ogihara, Mitsunori; Selman, Alan L.

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

*STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings.*vol. 665 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 665 LNCS, Springer Verlag, pp. 399-407, 10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993, Wurzburg, Germany, 2/25/93.

}

TY - GEN

T1 - On using oracles that compute values

AU - Fenner, Stephen

AU - Homer, Steve

AU - Ogihara, Mitsunori

AU - Selman, Alan L.

PY - 1993

Y1 - 1993

N2 - This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomial-time reducibilities, it is shown that 1. A multivalued partial function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable via 2k-1 nonadaptive queries to NPMV. 2. A characteristic function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable with k adaptive queries to NP. 3. Unless the Boolean hierarchy collapses, k adaptive (nonadaptive) queries to NPMV is different than k+1 adaptive (nonadaptive) queries to NPMV for every k. Nondeterministic reducibilities, lowness and the difference hierarchy over NPMV are also studied. The difference hierarchy for partial functions does not collapse unless the Boolean hierarchy collapses, but, surprisingly, the levels of the difference and bounded query hierarchies do not interleave (as is the case for sets) unless the polynomial hierarchy collapses.

AB - This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomial-time reducibilities, it is shown that 1. A multivalued partial function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable via 2k-1 nonadaptive queries to NPMV. 2. A characteristic function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable with k adaptive queries to NP. 3. Unless the Boolean hierarchy collapses, k adaptive (nonadaptive) queries to NPMV is different than k+1 adaptive (nonadaptive) queries to NPMV for every k. Nondeterministic reducibilities, lowness and the difference hierarchy over NPMV are also studied. The difference hierarchy for partial functions does not collapse unless the Boolean hierarchy collapses, but, surprisingly, the levels of the difference and bounded query hierarchies do not interleave (as is the case for sets) unless the polynomial hierarchy collapses.

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M3 - Conference contribution

SN - 9783540565031

VL - 665 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 399

EP - 407

BT - STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

PB - Springer Verlag

ER -