Counting Maximal Satisfiable Subsets

Given an unsatisfiable set of constraints F, a maximal satisfiable subset (MSS) is C ⊆ F such that satisfiable. Over the past two decades, steady improvement in runtime performance algorithms for finding MSS has led to increased adoption MSS-based techniques wide variety domains. Motivated by progress MSS, decade witnessed surge interest design algorithmic enumerate all MSSes, which subsequently discovery new applications utilizing enumeration MSSes. The development and MSSes mirrors similar phenomenon SAT solutions early 2000s, motivated model counting. In spirit, we undertake study investigate feasibility counting techniques. particular, focus point our investigation answer whether one can efficient do not rely on explicit enumeration. primary contribution this work affirmative above question. Our tool, CountMSS, uses novel architecture wrapper W remainder R desired count be expressed as |W| − |R|. CountMSS relies advances projected efficiently compute empirical evaluation demonstrates able scale instances clearly beyond reach enumeration-based