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A new upper bound for 3-SAT

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Abstract

We show that a randomly chosen $3$-CNF formula over $n$ variables with clauses-to-variables ratio at least $4.4898$ is asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was $4.506$. The first such bound, independently discovered by many groups of researchers since 1983, was $5.19$. Several decreasing values between $5.19$ and $4.506$ were published in the years between. The probabilistic techniques we use for the proof are, we believe, of independent interest.

BibTeX - Entry

@InProceedings{diaz_et_al:LIPIcs:2008:1750,
  author =	{Josep Diaz and Lefteris Kirousis and Dieter Mitsche and Xavier Perez-Gimenez},
  title =	{{A new upper bound for 3-SAT}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{163--174},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Ramesh Hariharan and Madhavan Mukund and V Vinay},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1750},
  URN =		{urn:nbn:de:0030-drops-17507},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2008.1750},
  annote =	{Keywords: Satisfiability, 3-SAT, random, threshold}
}

Keywords: Satisfiability, 3-SAT, random, threshold
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue date: 2008
Date of publication: 2008


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