On Deciding MUS Membership with QBF
نویسندگان
چکیده
This paper tackles the problem of deciding whether a given clause belongs to some minimally unsatisfiable subset (MUS) of a formula, where the formula is in conjunctive normal form (CNF) and unsatisfiable. Deciding MUS-membership helps the understanding of why a formula is unsatisfiable. If a clause does not belong to any MUS, then removing it will certainly not contribute to restoring the formula’s consistency. Unsatisfiable formulas and consistency restoration in particular have a number of practical applications in areas such as software verification or product configuration. The MUS-membership problem is known to be in the second level of polynomial hierarchy, more precisely it is Σ 2 -complete. Hence, quantified Boolean formulas (QBFs) represent a possible avenue for tackling the problem. This paper develops a number of novel QBF formulations of the MUS-membership problem and evaluates their practicality using modern off-the-shelf solvers.
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