On the maximum satisfiability of random formulas

摘要

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.