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Fixed-Parameter Tractable Reductions to SAT

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Theory and Applications of Satisfiability Testing – SAT 2014 (SAT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8561))

Abstract

Today’s SAT solvers have an enormous importance and impact in many practical settings. They are used as efficient back-end to solve many NP-complete problems. However, many computational problems are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. In certain cases one can break through these complexity barriers by fixed-parameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters. Recent research established a general theoretical framework that supports the classification of parameterized problems on whether they admit such an fpt-reduction to SAT or not. We use this framework to analyze some problems that are related to Boolean satisfiability. We consider several natural parameterizations of these problems, and we identify for which of these an fpt-reduction to SAT is possible. The problems that we look at are related to minimizing an implicant of a DNF formula, minimizing a DNF formula, and satisfiability of quantified Boolean formulas.

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Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Ronald de Haan & Stefan Szeider

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  1. Ronald de Haan
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  2. Stefan Szeider
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Editors and Affiliations

  1. Karlsruher Institut für Technologie (KIT), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Carsten Sinz

  2. TU Wien, Favoritenstraße 9-11, 1040, Wien, Austria

    Uwe Egly

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de Haan, R., Szeider, S. (2014). Fixed-Parameter Tractable Reductions to SAT. In: Sinz, C., Egly, U. (eds) Theory and Applications of Satisfiability Testing – SAT 2014. SAT 2014. Lecture Notes in Computer Science, vol 8561. Springer, Cham. https://doi.org/10.1007/978-3-319-09284-3_8

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  • DOI: https://doi.org/10.1007/978-3-319-09284-3_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09283-6

  • Online ISBN: 978-3-319-09284-3

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