Global Optimization for Satisfiability (SAT) Problem

The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and D N F local search methods, we introduce the Universal SAT problem model, UniSAT, which transforms the discrete SAT problem on Boolean space (0, l}"' into an unconstrained global optimization problem on real space E"'. A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtrackinglresolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF) formulas. It offers a complementary approach to the existing SAT algorithms.