Proof-Stitch: Proof Combination for Divide and Conquer SAT Solvers

Abstract: With the increasing availability of parallel computing power, there is a growing focus on parallelizing algorithms for important automated reasoning problems such as Boolean satisfiability (SAT). Divide-and-Conquer (D&C) is a popular parallel SAT solving paradigm that partitions SAT instances into independent sub-problems which are then solved in parallel. For unsatisfiable instances, state-of-the-art D&C solvers generate DRAT refutations for each sub-problem. However, they do not generate a single refutation for the original instance. To close this gap, we present Proof-Stitch, a procedure for combining refutations of different sub-problems into a single refutation for the original instance. We prove the correctness of the procedure and propose optimizations to reduce the size and checking time of the combined refutations by invoking existing trimming tools in the proof-combination process. We also provide an extensible implementation of the proposed technique. Experiments on instances from last year's SAT competition show that the optimized refutations are checkable up to seven times faster than unoptimized refutations.