Boosting minimal unsatisfiable core extraction

A variety of tasks in formal verification require finding small or minimal unsatisfiable cores (subsets) of an unsatisfiable set of constraints. This paper proposes two algorithms for finding a minimal unsatisfiable core or, if a time-out occurs, a small non-minimal unsatisfiable core. Our algorithms can be applied to either standard clause-level unsatisfiable core extraction or high-level unsatisfiable core extraction, that is, an extraction of an unsatisfiable core in terms of “interesting” propositional constraints supplied by the user application. We demonstrate that one of our algorithms outperforms existing algorithms for clause-level minimal unsatisfiable core extraction on large well-known industrial benchmarks. We also show that our algorithms are highly scalable for the problem of high-level minimal unsatisfiable core extraction on huge benchmarks generated by Intel's proof-based abstraction refinement flow. In addition, we provide a comparative analysis of the impact of various algorithms on unsatisfiable core extraction.