On the satisfiability threshold of formulas with three literals per clause,☆☆

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Abstract

In this paper we present a new upper bound for randomly chosen 3-CNF formulas. In particular we show that any random formula over n variables, with a clauses-to-variables ratio of at least 4.4898 is, as n grows large, 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. We believe that the probabilistic techniques we use for the proof are of independent interest.

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Partially supported by the Spanish CYCIT: TIN2007-66523 (FORMALISM). The first and second authors were also partially supported by the EU within the 7th Framework Programme under contract 215270 (FRONTS).

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An extended abstract of this paper was accepted for presentation at FSTTCS-08.