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MCS Extraction with Sublinear Oracle Queries

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Theory and Applications of Satisfiability Testing – SAT 2016 (SAT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9710))

Abstract

Given an inconsistent set of constraints, an often studied problem is to compute an irreducible subset of the constraints which, if relaxed, enable the remaining constraints to be consistent. In the case of unsatisfiable propositional formulas in conjunctive normal form, such irreducible sets of constraints are referred to as Minimal Correction Subsets (MCSes). MCSes find a growing number of applications, including the approximation of maximum satisfiability and as an intermediate step in the enumeration of minimal unsatisfiability. A number of efficient algorithms have been proposed in recent years, which exploit a wide range of insights into the MCS extraction problem. One open question is to find the best worst-case number of calls to a SAT oracle, when the calls to the oracle are kept simple, and given reasonable definitions of simple SAT oracle calls. This paper develops novel algorithms for computing MCSes which, in specific settings, are guaranteed to require asymptotically fewer than linear calls to a SAT oracle, where the oracle calls can be viewed as simple. The experimental results, obtained on existing problem instances, demonstrate that the new algorithms contribute to improving the state of the art.

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Notes

  1. 1.

    This is the case for example with the analysis of infeasible systems of linear inequalities [10].

  2. 2.

    Nevertheless, irreducible inconsistent sets of linear inequalities have been studied for more than a century [10].

  3. 3.

    By exploiting the reduction of MCS extraction to MSMP [29], a wealth of different MUS extraction algorithms can be used for MCS extraction, including the insertion-based algorithm.

  4. 4.

    Available at http://logos.ucd.ie/web/doku.php?id=mcsxl.

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Acknowledgement

This work was partly funded by grant TIN2013-46511-C2-2-P.

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Authors and Affiliations

  1. LaSIGE, Faculty of Science, University of Lisbon, Lisbon, Portugal

    Alexey Ignatiev, Alessandro Previti & Joao Marques-Silva

  2. University of Oviedo, Gijón, Spain

    Carlos Mencía

  3. ISDCT SB RAS, Irkutsk, Russia

    Alexey Ignatiev

Authors
  1. Carlos Mencía
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  2. Alexey Ignatiev
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  3. Alessandro Previti
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  4. Joao Marques-Silva
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Correspondence to Carlos Mencía .

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Editors and Affiliations

  1. Aix-Marseille Université, Marseille, France

    Nadia Creignou

  2. Université d'Artois, Lens, France

    Daniel Le Berre

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Mencía, C., Ignatiev, A., Previti, A., Marques-Silva, J. (2016). MCS Extraction with Sublinear Oracle Queries. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_21

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  • DOI: https://doi.org/10.1007/978-3-319-40970-2_21

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