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Generalized Modal Satisfiability

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STACS 2006 (STACS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

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Abstract

It is well-known that modal satisfiability is PSPACE-complete [Lad77]. However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits.

Supported in part by grants NSF-CCR-0311021 and DFG VO 630/5-1.

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Hannover, Appelstr. 4, 30167, Hannover, Germany

    Michael Bauland, Henning Schnoor & Ilka Schnoor

  2. Department of Computer Science, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Edith Hemaspaandra

Authors
  1. Michael Bauland
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  2. Edith Hemaspaandra
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  3. Henning Schnoor
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  4. Ilka Schnoor
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Editor information

Editors and Affiliations

  1. LIF, CNRS & Univ. de Provence,, Marseille, France

    Bruno Durand

  2. RWTH Aachen University,, Lehrstuhl Informatik 7,, 52056,, Aachen,, Germany

    Wolfgang Thomas

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© 2006 Springer-Verlag Berlin Heidelberg

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Bauland, M., Hemaspaandra, E., Schnoor, H., Schnoor, I. (2006). Generalized Modal Satisfiability. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_41

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  • DOI: https://doi.org/10.1007/11672142_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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