On Computing Minimal Correction Subsets

Abstract

A set of constraints that cannot be simultaneously satisfied is over-constrained. Minimal relaxations and minimal explanations for over-constrained problems find many practical uses. For Boolean formulas, minimal relaxations of over-constrained problems are referred to as Minimal Correction Subsets (MCSes). MCSes find many applications, including the enumeration of MUSes. Existing approaches for computing MCSes either use a Maximum Satisfiability (MaxSAT) solver or iterative calls to a Boolean Satisfiability (SAT) solver. This paper shows that existing algorithms for MCS computation can be inefficient, and so inadequate, in certain practical settings. To address this problem , this paper develops a number of novel techniques for improving the performance of existing MCS computation algorithms. More importantly, the paper proposes a novel algorithm for computing MCSes. Both the techniques and the algorithm are evaluated empirically on representative problem instances , and are shown to yield the most efficient and robust solutions for MCS computation.

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