Local Search with Bootstrapping

We propose and study a technique to improve the performance of those local-search SAT solvers that proceed by executing a prespecified number of tries, each starting with an element of the space of all truth assignments and performing a prespecified number of local-search steps (flips). Based on the input theory T, our method first constructs a collection of its relaxations, that is, theories whose models are easy to compute and “almost” satisfy T. It then uses a local-search algorithm to compute models of the relaxed theories and, finally, uses these models as starting points for tries when executing the local search algorithm on T. To construct relaxations our method takes advantage of high-level representation of search problems, which separate the specification of a search problem from the description of its particular instances. The method is general. We applied it to WSAT, a local-search SAT solver for CNF theories, and to WSAT(cc), a local-search SAT algorithm for theories in the language of propositional logic with cardinality constraints. Experimental results demonstrate its effectiveness for both local-search algorithms we studied.