Approximating Satissable Satissability Problems

We study the approximability of the Maximum Satissability Problem (Max SAT) and of the boolean k-ary Constraint Satisfaction Problem (Max kCSP) restricted to satissable instances. For both problems we improve on the performance ratios of known algorithms for the unrestricted case. Our approximation for satissable Max 3CSP instances is better than any possible approximation for the unrestricted version of the problem (unless P = NP). This result implies that the requirement of perfect completeness weakens the acceptance power of non-adaptive PCP veriiers that read 3 bits. We also present the rst non-trivial results about PCP classes deened in terms of free bits that collapse to P.

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