Finding Unsatisfiable Subformulas with Stochastic Method

Abstract. Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. A small unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. In recent years the problem of finding unsatisfiable subformulas has been addressed frequently by research works, which are mostly based on the SAT solvers with DPLL backtrack-search algorithm. However little attention has been concentrated on extraction of unsatisfiable subformulas using stochastic methods. In this paper, we propose a resolution-based stochastic local search algorithm to derive unsatisfiable subformulas. This approach directly constructs the resolution sequences for proving unsatisfiability with a local search procedure, and then extracts small unsatisfiable subformulas from the refutation traces. We report and analyze the experimental results on benchmarks