MCS Extraction with Sublinear Oracle Queries

Abstract

Given an inconsistent set of constraints, an often studied problem is to compute an irreducible subset of the constraints which, if relaxed, enable the remaining constraints to be consistent. In the case of unsatisfiable propositional formulas in conjunctive normal form, such irreducible sets of constraints are referred to as Minimal Correction Subsets (MCSes). MCSes find a growing number of applications, including the approximation of maximum satisfiability and as an intermediate step in the enumeration of minimal unsatisfiability. A number of efficient algorithms have been proposed in recent years, which exploit a wide range of insights into the MCS extraction problem. One open question is to find the best worst-case number of calls to a SAT oracle, when the calls to the oracle are kept simple, and given reasonable definitions of simple SAT oracle calls. This paper develops novel algorithms for computing MCSes which, in specific settings, are guaranteed to require asymptotically fewer than linear calls to a SAT oracle, where the oracle calls can be viewed as simple. The experimental results, obtained on existing problem instances, demonstrate that the new algorithms contribute to improving the state of the art.