Solving Difficult SAT Instances Using Greedy Clique Decomposition

Abstract

We are dealing with solving difficult SAT instances in this paper. We propose a method for preprocessing SAT instances (CNF formulas) by using consistency techniques known from constraint programming methodology and by using our own consistency technique based on clique decomposition of a graph representing conflicts in the input formula. If the clique decomposition is of a good quality (cliques are appropriately large) it then allows us to make a strong reasoning over the SAT instance, which can in some cases even decide the satisfiability of the SAT instance without search. We implemented our preprocessing method in C++ and compared it with several state-of-the-art SAT solvers on selected difficult SAT instances. The result was a speedup in the order of magnitude compared to the tested SAT solvers.