A New Exact Bit-Parallel Algorithm for SAT

This paper presents two new exact general purpose bit-parallel algorithms (BB-SAT and BBP-SAT) for the Boolean satisfiability problem (SAT). Based on the authors' recent successful bit-parallel algorithm for the maximum clique problem, the SAT formula is first reduced to a directed graph which is then bit encoded. As a result, search traverses a bit vector graph space. At present the encoding allows for an efficient bitwise computation of graph state transitions as well as unit clause and pure literal evaluation. Experiments carried out on a number of DIMACS instances are highly encouraging since BBP-SAT is already reasonably competitive employing just basic DPLL tactics with minor refinements. BBP-SAT is a fresh approach in an otherwise mature domain. Further additional bit encoded knowledge of the more recent successful SAT algorithms (e.g. bit parallel heuristic variable selection) should make BBP-SAT a competitive general purpose solver.