Distributed Parallel #SAT Solving

The #SAT problem, that is counting the number of solutions of a propositional formula, extends the well-known SAT problem into the realm of probabilistic reasoning. However, the higher computational complexity and lack of fast solvers still limits its applicability for real world problems. In this work we present our distributed parallel #SAT solver dCountAntom which utilizes both local, shared-memory parallelism as well as distributed (cluster computing) parallelism. Although highly parallel solvers are known in SAT solving, such techniques have never been applied to the #SAT problem. Furthermore we introduce a solve progress indicator which helps the user to assess whether the presented problem is likely solvable within a reasonable time. Our analysis shows a high accuracy of the estimated progress. Our experiments with up to 256 CPU cores working in parallel yield large speedups across different benchmarks derived from real world problems: With the maximum number of available cores dCountAntom solved problems on average 141 times faster than a single core implementation.