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On exact selection of minimally unsatisfiable subformulae

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Abstract

A minimally unsatisfiable subformula (MUS) is a subset of clauses of a given CNF formula which is unsatisfiable but becomes satisfiable as soon as any of its clauses is removed. The selection of a MUS is of great relevance in many practical applications. This expecially holds when the propositional formula encoding the application is required to have a well-defined satisfiability property (either to be satisfiable or to be unsatisfiable). While selection of a MUS is a hard problem in general, we show classes of formulae where this problem can be solved efficiently. This is done by using a variant of Farkas’ lemma and solving a linear programming problem. Successful results on real-world contradiction detection problems are presented.

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  1. Dipartimento di Informatica e Sistemistica, Università; di Roma “La Sapienza”, Via Buonarroti 12, 00185, Roma, Italy

    Renato Bruni

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  1. Renato Bruni
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Bruni, R. On exact selection of minimally unsatisfiable subformulae. Ann Math Artif Intell 43, 35–50 (2005). https://doi.org/10.1007/s10472-005-0418-4

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  • DOI: https://doi.org/10.1007/s10472-005-0418-4

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