A Heuristic Local Search Algorithm for Unsatisfiable Cores Extraction

Abstract

Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. We are generally interested in a small explanation of unsatisfiability that excludes irrelevant information. A small unsatisfiable core 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 cores using incomplete methods. In this paper, we propose a heuristic-based local search algorithm to derive unsatisfiable cores. This approach directly constructs the resolution sequence for proving unsatisfiability with a local search procedure, and then extracts small unsatisfiable cores from the sequence. We report and analyze the experimental results on benchmarks.