Stochastic Local Search for SMT: Combining Theory Solvers with WalkSAT

Abstract

A dominant approach to Satisfiability Modulo Theories (SMT) relies on the integration of a Conflict-Driven-Clause-Learning (CDCL) SAT solver and of a decision procedure able to handle sets of atomic constraints in the underlying theory \(\mathcal{T}\) (\({\ensuremath{\mathcal{T}} }\textit{-solver}\) ). In pure SAT, however, Stochastic Local-Search (SLS) procedures sometimes are competitive with CDCL SAT solvers on satisfiable instances. Thus, it is a natural research question to wonder whether SLS can be exploited successfully also inside SMT tools.In this paper we investigate this issue. We first introduce a general procedure for integrating a SLS solver of the WalkSAT family with a \({\ensuremath{\mathcal{T}} }\textit{-solver}\). Then we present a group of techniques aimed at improving the synergy between these two components. Finally we implement all these techniques into a novel SLS-based SMT solver for the theory of linear arithmetic over the rationals, combining UBCSAT/UBCSAT++ and MathSAT, and perform an empirical evaluation on satisfiable instances. The results confirm the potential of the approach.KeywordsTruth AssignmentUnit ClauseStochastic Local SearchMultiple LearnInput FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.