### 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 |

Editors | Ding-Zhu Du, Ding-Zhu Du, Xiang-Sun Zhang |

Publisher | Springer Verlag |

Pages | 57-64 |

Number of pages | 8 |

ISBN (Print) | 9783540583257 |

DOIs | |

State | Published - Jan 1 1994 |

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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Computing solutions uniquely collapses the polynomial hierarchy'. Together they form a unique fingerprint.

## Cite this

Hemaspaandra, L. A., Naik, A. V., Ogihara, M., & Selman, A. L. (1994). Computing solutions uniquely collapses the polynomial hierarchy. In D-Z. Du, D-Z. Du, & X-S. Zhang (Eds.),

*Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings*(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. https://doi.org/10.1007/3-540-58325-4_166