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On Deciding MUS Membership with QBF

  • Conference paper
Principles and Practice of Constraint Programming – CP 2011 (CP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6876))

Abstract

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 \(\Sigma{^p_2}\) -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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Author information

Authors and Affiliations

  1. INESC-ID, Lisbon, Portugal

    Mikoláš Janota & Joao Marques-Silva

  2. University College Dublin, Ireland

    Joao Marques-Silva

Authors
  1. Mikoláš Janota
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  2. Joao Marques-Silva
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

    Jimmy Lee

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Janota, M., Marques-Silva, J. (2011). On Deciding MUS Membership with QBF. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_32

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  • DOI: https://doi.org/10.1007/978-3-642-23786-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23785-0

  • Online ISBN: 978-3-642-23786-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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