### 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) |
---|---|

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) |
---|---|

Volume | 1893 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

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

Country | Slovakia |

City | Bratislava |

Period | 8/28/00 → 9/1/00 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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

**Reducing the number of solutions of NP functions?** / Hemaspaandra, Lane A.; Ogihara, Mitsunori; Wechsung, Gerd.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 1893, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1893, Springer Verlag, pp. 394-404, 25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000, Bratislava, Slovakia, 8/28/00. https://doi.org/10.1007/3-540-44612-5_35

}

TY - GEN

T1 - Reducing the number of solutions of NP functions?

AU - Hemaspaandra, Lane A.

AU - Ogihara, Mitsunori

AU - Wechsung, Gerd

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84959224631&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959224631&partnerID=8YFLogxK

U2 - 10.1007/3-540-44612-5_35

DO - 10.1007/3-540-44612-5_35

M3 - Conference contribution

AN - SCOPUS:84959224631

SN - 3540679014

VL - 1893

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

SP - 394

EP - 404

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

PB - Springer Verlag

ER -