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A new upper bound for 3-SAT

Authors Josep Diaz, Lefteris Kirousis, Dieter Mitsche, Xavier Perez-Gimenez



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LIPIcs.FSTTCS.2008.1750.pdf
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Author Details

Josep Diaz
Lefteris Kirousis
Dieter Mitsche
Xavier Perez-Gimenez

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Josep Diaz, Lefteris Kirousis, Dieter Mitsche, and Xavier Perez-Gimenez. A new upper bound for 3-SAT. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 163-174, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1750

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.
Keywords
  • Satisfiability
  • 3-SAT
  • random
  • threshold

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