Reducing the number of solutions of NP functions?

Lane A. Hemaspaandra, Mitsunori Ogihara, Gerd Wechsung

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages394-404
Number of pages11
Volume1893
ISBN (Print)3540679014
DOIs
StatePublished - 2000
Externally publishedYes
Event25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000 - Bratislava, Slovakia
Duration: Aug 28 2000Sep 1 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1893
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000
CountrySlovakia
City Bratislava
Period8/28/009/1/00

Fingerprint

Number of Solutions
Polynomial Hierarchy
Complexity Classes
Cardinality
Necessary Conditions
Path
Sufficient Conditions
Polynomials

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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

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

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1893 Springer Verlag, 2000. p. 394-404 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1893).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hemaspaandra, LA, 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, 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
Hemaspaandra LA, Ogihara M, Wechsung G. 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. Springer Verlag. 2000. p. 394-404. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-44612-5_35
Hemaspaandra, Lane A. ; Ogihara, Mitsunori ; Wechsung, Gerd. / Reducing the number of solutions of NP functions?. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1893 Springer Verlag, 2000. pp. 394-404 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{62adbd92a80e4758ac65501891a3c979,
title = "Reducing the number of solutions of NP functions?",
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.",
author = "Hemaspaandra, {Lane A.} and Mitsunori Ogihara and Gerd Wechsung",
year = "2000",
doi = "10.1007/3-540-44612-5_35",
language = "English (US)",
isbn = "3540679014",
volume = "1893",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "394--404",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

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 -