Approximating satisfiable satisfiability problems

Abstract

We study the approximabflity of the Maximum Satisfiability Problem (MAx SAT) and of the boolean k-ary Constraint Satisfaction Problem (MAX kCSP) restricted to satisfiable instances. For both problems we improve on the performance ratios of known algorithms for the unrestricted case. Our approximation for satisfiable MAX 3CSP instances is better than any possible approximation for the unrestricted version of the problem (unless P= NP). This result implies that the requirements of perfect completeness and non-adaptiveness weaken the acceptance power of PCP verifiers. We also present the first non-trivial results about PCP classes defined in terms of free bits that collapse to P.