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Using heuristics to find minimal unsatisfiable subformulas in satisfiability problems

Author

Listed:
  • Christian Desrosiers

    (Ecole Polytechnique and GERAD)

  • Philippe Galinier

    (Ecole Polytechnique and CRT)

  • Alain Hertz

    (Ecole Polytechnique and GERAD)

  • Sandrine Paroz

    (Ecole Polytechnique and GERAD)

Abstract

In this paper, we propose efficient algorithms to extract minimal unsatisfiable subsets of clauses or variables in unsatisfiable propositional formulas. Such subsets yield unsatisfiable propositional subformulas that become satisfiable when any of their clauses or variables is removed. These subformulas have numerous applications, including proving unsatisfiability and post-infeasibility analysis. The algorithms we propose are based on heuristics, and thus, can be applied to large instances. Furthermore, we show that, in some cases, the minimality of the subformulas can be proven with these algorithms. We also present an original algorithm to find minimum cardinality unsatisfiable subformulas in smaller instances. Finally, we report computational experiments on unsatisfiable instances from various sources, that demonstrate the effectiveness of our algorithms.

Suggested Citation

  • Christian Desrosiers & Philippe Galinier & Alain Hertz & Sandrine Paroz, 2009. "Using heuristics to find minimal unsatisfiable subformulas in satisfiability problems," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 124-150, August.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:2:d:10.1007_s10878-008-9142-4
    DOI: 10.1007/s10878-008-9142-4
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    References listed on IDEAS

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    1. John Gleeson & Jennifer Ryan, 1990. "Identifying Minimally Infeasible Subsystems of Inequalities," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 61-63, February.
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    Cited by:

    1. Wen Sun & Jin-Kao Hao & Alexandre Caminada, 2019. "Iterated backtrack removal search for finding k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 25(4), pages 565-590, October.

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