On Computing Preferred MUSes and MCSes

ABSTRACT. Minimal Unsatisfiable Subsets (MUSes) and Minimal Correction Subsets (MCSes) are essential tools for the analysis of unsatisfiable formulas. MUSes and MCSes find a growing number of applications, that include abstraction refinement in software verification, type debugging, software package management and software configuration, among many others. In some applications, there can exist preferences over which clauses to include in computed MUSes or MCSes, but also in computed Maximal Satisfiable Subsets (MSSes). Moreover, different definitions of preferred MUSes, MCSes and MSSes can be considered. This paper revisits existing definitions of preferred MUSes, MCSes and MSSes of unsatisfiable formulas, and develops a preliminary characterization of the computational complexity of computing preferred MUSes, MCSes and MSSes. Moreover, the paper investigates which of the existing algorithms and pruning techniques can be applied for computing preferred MUSes, MCSes and MSSes. Finally, the paper shows that the computation of preferred sets can have significant impact in practical performance.