Systematic versus Local Search and GA Techniques for Incremental SAT

Propositional satisfiability (SAT) problem is fundamental to the theory of NP-completeness. Indeed, using the concept of ”polynomial-time reducibility” all NP-complete problems can be polynomially reduced to SAT. Thus, any new technique for satisfiability problems will lead to general approaches for thousands of hard combinatorial problems. In this paper, we introduce the incremental propositional satisfiability problem that consists of maintaining the satisfiability of a propositional formula anytime a conjunction of new clauses is added. More precisely, the goal here is to check whether a solution to a SAT problem continues to be a solution anytime a new set of clauses is added and if not, whether the solution can be modified efficiently to satisfy the old formula and the new clauses. We will study the applicability of systematic and approximation methods for solving incremental SAT problems. The systematic method is based on the branch and bound technique while the approximation methods rely on stochastic local search (SLS) and genetic algorithms (GA). A comprehensive empirical study, conducted on a wide range of randomly generated consistent SAT instances, demonstrates the efficiency in time of the approximation methods over the branch and bound algorithm. However these approximation methods do not guarantee the completeness of the solution returned. We show that a method we propose that uses non systematic search in a limited form together with branch and bound has the best compromise, in practice, between time and the success ratio (percentage of instances completely solved).