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The Complexity of Problems for Quantified Constraints

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Abstract

In this paper we are interested in quantified propositional formulas in conjunctive normal form with “clauses” of arbitrary shapes. i.e., consisting of applying arbitrary relations to variables. We study the complexity of the evaluation problem, the model checking problem, the equivalence problem, and the counting problem for such formulas, both with and without a bound on the number of quantifier alternations. For each of these computational goals we get full complexity classifications: We determine the complexity of each of these problems depending on the set of relations allowed in the input formulas. Thus, on the one hand we exhibit syntactic restrictions of the original problems that are still computationally hard, and on the other hand we identify non-trivial subcases that admit efficient algorithms.

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Authors and Affiliations

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

    Michael Bauland, Henning Schnoor & Heribert Vollmer

  2. Elektrobit Automotive Software, Am Wolfsmantel, 91058, Erlangen, Germany

    Elmar Böhler

  3. Aix-Marseille Université, 163 av. de Luminy, 13288, Marseille, France

    Nadia Creignou

  4. Fachbereich Design Informatik Medien, University of Applied Sciences, Kurt-Schumacher-Ring 18, 65198, Wiesbaden, Germany

    Steffen Reith

Authors
  1. Michael Bauland
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  2. Elmar Böhler
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  3. Nadia Creignou
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  4. Steffen Reith
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  5. Henning Schnoor
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  6. Heribert Vollmer
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Correspondence to Heribert Vollmer.

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Supported in part by the following grants: DFG Vo 630/5-1, 630/5-2, ÉGIDE 05835SH, DAAD D/0205776.

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Bauland, M., Böhler, E., Creignou, N. et al. The Complexity of Problems for Quantified Constraints. Theory Comput Syst 47, 454–490 (2010). https://doi.org/10.1007/s00224-009-9194-6

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  • DOI: https://doi.org/10.1007/s00224-009-9194-6

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