### Abstract

We study whether one can prune solutions from NP functions. Though it is known that, unless surprising complexity class collapses occur, one cannot reduce the number of accepting paths of NP machines [17], we nonetheless show that it often is possible to reduce the number of solutions of NP functions. For finite cardinality types, we give a sufficient condition for such solution reduction. We also give absolute and conditional necessary conditions for solution reduction, and in particular we show that in many cases solution reduction is impossible unless the polynomial hierarchy collapses.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 394-404 |

Number of pages | 11 |

Volume | 1893 |

ISBN (Print) | 3540679014 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

Event | 25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000 - Bratislava, Slovakia Duration: Aug 28 2000 → Sep 1 2000 |

### 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 | 1893 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000 |
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Country | Slovakia |

City | Bratislava |

Period | 8/28/00 → 9/1/00 |

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

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## Cite this

Hemaspaandra, L. A., Ogihara, M., & Wechsung, G. (2000). Reducing the number of solutions of NP functions? In

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 1893, pp. 394-404). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1893). Springer Verlag. https://doi.org/10.1007/3-540-44612-5_35