On the maximum satisfiability of random formulas

D. Achlioptas, A. Naor, Y. Peres

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

Abstract

Maximum satisfiability is a canonical NP-complete problem that appears empirically hard for random instances. At the same time, it is rapidly becoming a canonical problem for statistical physics. In both of these realms, evaluating new ideas relies crucially on knowing the maximum number of clauses one can typically satisfy in a random k-CNF formula. In this paper we give asymptotically tight estimates for this quantity. Our result gives very tight bounds for the fraction of satisfiable clauses in a random k-CNF. In particular, for k > 2 it improves upon all previously known such bound.

Original languageEnglish (US)
Title of host publicationProceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003
PublisherIEEE Computer Society
Pages362-370
Number of pages9
Volume2003-January
ISBN (Print)0769520405
DOIs
StatePublished - 2003
Event44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 - Cambridge, United States
Duration: Oct 11 2003Oct 14 2003

Other

Other44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003
CountryUnited States
CityCambridge
Period10/11/0310/14/03

Fingerprint

Computational complexity
Physics

Keywords

  • Benchmark testing
  • Computer science
  • Glass
  • H infinity control
  • Mathematics
  • NP-complete problem
  • Operations research
  • Physics
  • Stationary state
  • Statistics

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Achlioptas, D., Naor, A., & Peres, Y. (2003). On the maximum satisfiability of random formulas. In Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 (Vol. 2003-January, pp. 362-370). [1238210] IEEE Computer Society. https://doi.org/10.1109/SFCS.2003.1238210

On the maximum satisfiability of random formulas. / Achlioptas, D.; Naor, A.; Peres, Y.

Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003. Vol. 2003-January IEEE Computer Society, 2003. p. 362-370 1238210.

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

Achlioptas, D, Naor, A & Peres, Y 2003, On the maximum satisfiability of random formulas. in Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003. vol. 2003-January, 1238210, IEEE Computer Society, pp. 362-370, 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003, Cambridge, United States, 10/11/03. https://doi.org/10.1109/SFCS.2003.1238210
Achlioptas D, Naor A, Peres Y. On the maximum satisfiability of random formulas. In Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003. Vol. 2003-January. IEEE Computer Society. 2003. p. 362-370. 1238210 https://doi.org/10.1109/SFCS.2003.1238210
Achlioptas, D. ; Naor, A. ; Peres, Y. / On the maximum satisfiability of random formulas. Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003. Vol. 2003-January IEEE Computer Society, 2003. pp. 362-370
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