An Efficient Resolution Based Algorithm for SAT

Propositional satisfiability problem (SAT) is a fundamental problem both in theory and practice. In the area of software engineering, people employ various techniques, such as model checking, theorem proving, automated testing and so on, to ensure the quality of software. Those techniques are usually based on SAT solvers. The efficiency is an important criterion for a good SAT solver. Besides, the ability of producing proofs is also considered to be quite useful because it provides a mechanism that the correctness of checking result is guaranteed. Moreover, proofs can be used when calculating interpolation. In this paper, we investigate a new resolution based algorithm for solving SAT problem. The algorithm combines resolution and search. It resolves certain clauses when necessary and at the same time tries to find a valuation under which the formula evaluates to true. Information found in the process of searching for such a valuation is used to guide the resolution. The algorithm stops whenever a satisfying valuation is found or empty clause is generated. So, it terminates quickly for both satisfiable and unsatisfiable clauses. Compared with other resolution based algorithms, the experiment result shows that the number of resolutions and number of generated clauses are much less than directional resolution. Another major advantage of our algorithm is, once terminates, a proof can be easily generated with very low time complexity.