Overcoming Resolution-Based Lower Bounds for SAT Solvers

Many leading-edge SAT solvers are based on the Davis-Putnam procedure or the Davis-Logemann-Loveland procedure, and thus on unsatisfiable instances they can be viewed as attempting to find refutations by resolution. Therefore, exponential lower bounds on the length of resolution proofs also apply to such solvers. Empirical performance of DLL-based solvers on SAT instances from the pigeonhole and Urquhart family are consistent with this expectation. Our work explores an entirely different approach to SAT solving that does not have this drawback. A bare-bones implementation of our algorithm, reported earlier, was able to refute pigeonhole instances in polynomial time without explicitly using symmetries, and this empirical result is backed up by an analytical proof. In this work, we show how to extend Compressed-BFS to perform Boolean Constraint Propagation, part of all practical, complete SAT solvers. Unlike DLL-based solvers, our empirical results show that full BCP offers marginal improvements in runtime.