On the satisfiability threshold of formulas with three literals per clause

Authors:
J. Díaz;L. Kirousis;D. Mitsche;X. Pérez-Giménez
Affiliations:
Llenguatges i Sistemes Informàtics, UPC, 08034 Barcelona, Spain;RA Computer Technology Institute, GR-26504 Rio, Patras, Greece and Computer Engineering and Informatics, University of Patras, GR-26504 Rio, Patras, Greece;Llenguatges i Sistemes Informàtics, UPC, 08034 Barcelona, Spain;Llenguatges i Sistemes Informàtics, UPC, 08034 Barcelona, Spain
Venue:
Theoretical Computer Science
Year:
2009

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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.