### Abstract

We show that if there is an NP function that, when given a satisfiable formula as input, outputs one satisfying assignment uniquely, then the polynomial hierarchy collapses to its second level. As the existence of such a function is known to be equivalent to the statement “every NP function has an NP refinement with unique outputs,” our result provides the strongest evidence yet that NP functions cannot be refined.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings |

Publisher | Springer Verlag |

Pages | 57-64 |

Number of pages | 8 |

Volume | 834 LNCS |

ISBN (Print) | 9783540583257 |

State | Published - 1994 |

Externally published | Yes |

Event | 5th Annual International Symposium on Algorithms and Computation, ISAAC 1994 - Beijing, China Duration: Aug 25 1994 → Aug 27 1994 |

### 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 | 834 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th Annual International Symposium on Algorithms and Computation, ISAAC 1994 |
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Country | China |

City | Beijing |

Period | 8/25/94 → 8/27/94 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings*(Vol. 834 LNCS, pp. 57-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 834 LNCS). Springer Verlag.

**Computing solutions uniquely collapses the polynomial hierarchy.** / Hemaspaandra, Lane A.; Naik, Ashish V.; Ogihara, Mitsunori; Selman, Alan L.

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

*Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings.*vol. 834 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 834 LNCS, Springer Verlag, pp. 57-64, 5th Annual International Symposium on Algorithms and Computation, ISAAC 1994, Beijing, China, 8/25/94.

}

TY - GEN

T1 - Computing solutions uniquely collapses the polynomial hierarchy

AU - Hemaspaandra, Lane A.

AU - Naik, Ashish V.

AU - Ogihara, Mitsunori

AU - Selman, Alan L.

PY - 1994

Y1 - 1994

N2 - We show that if there is an NP function that, when given a satisfiable formula as input, outputs one satisfying assignment uniquely, then the polynomial hierarchy collapses to its second level. As the existence of such a function is known to be equivalent to the statement “every NP function has an NP refinement with unique outputs,” our result provides the strongest evidence yet that NP functions cannot be refined.

AB - We show that if there is an NP function that, when given a satisfiable formula as input, outputs one satisfying assignment uniquely, then the polynomial hierarchy collapses to its second level. As the existence of such a function is known to be equivalent to the statement “every NP function has an NP refinement with unique outputs,” our result provides the strongest evidence yet that NP functions cannot be refined.

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UR - http://www.scopus.com/inward/citedby.url?scp=79151486077&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79151486077

SN - 9783540583257

VL - 834 LNCS

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

SP - 57

EP - 64

BT - Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings

PB - Springer Verlag

ER -