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Parameterized Complexity of Weighted Satisfiability Problems

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Theory and Applications of Satisfiability Testing – SAT 2012 (SAT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7317))

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Abstract

We consider the weighted satisfiability problem for Boolean circuits and propositional formulæ, where the weight of an assignment is the number of variables set to true. We study the parameterized complexity of these problems and initiate a systematic study of the complexity of its fragments. Only the monotone fragment has been considered so far and proven to be of same complexity as the unrestricted problems. Here, we consider all fragments obtained by semantically restricting circuits or formulæ to contain only gates (connectives) from a fixed set B of Boolean functions. We obtain a dichotomy result by showing that for each such B, the weighted satisfiability problems are either W[P]-complete (for circuits) or W[SAT]-complete (for formulæ) or efficiently solvable. We also consider the related counting problems.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Fondamentale de Marseille, CNRS UMR 7279, Aix-Marseille Université, 163 avenue de Luminy, F-13288, Marseille Cedex 9, France

    Nadia Creignou

  2. Institut für Theoretische Informatik, Leibniz Universität Hannover, Appelstr. 4, 30167, Hannover, Germany

    Heribert Vollmer

Authors
  1. Nadia Creignou
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  2. Heribert Vollmer
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Editor information

Editors and Affiliations

  1. Center for Information Technology, Fondazione Bruno Kessler, via Sommarive 18, Povo, 38123, Trento, Italy

    Alessandro Cimatti

  2. Department of Information Engineering and Computer Science, University of Trento, via Sommarive 14, Povo, 38123, Trento, Italy

    Roberto Sebastiani

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Creignou, N., Vollmer, H. (2012). Parameterized Complexity of Weighted Satisfiability Problems. In: Cimatti, A., Sebastiani, R. (eds) Theory and Applications of Satisfiability Testing – SAT 2012. SAT 2012. Lecture Notes in Computer Science, vol 7317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31612-8_26

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  • DOI: https://doi.org/10.1007/978-3-642-31612-8_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31611-1

  • Online ISBN: 978-3-642-31612-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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