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Fixpoint Logics over Hierarchical Structures

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Abstract

Hierarchical graph definitions allow a modular description of graphs using modules for the specification of repeated substructures. Beside this modularity, hierarchical graph definitions also allow to specify graphs of exponential size using polynomial size descriptions. In many cases, this succinctness increases the computational complexity of decision problems. In this paper, the model-checking problem for the modal μ-calculus and (monadic) least fixpoint logic on hierarchically defined input graphs is investigated. In order to analyze the modal μ-calculus, parity games on hierarchically defined input graphs are investigated. Precise upper and lower complexity bounds are derived. A restriction on hierarchical graph definitions that leads to more efficient model-checking algorithms is presented.

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Authors and Affiliations

  1. Fachbereich 3, Universität Bremen, Bremen, Germany

    Stefan Göller

  2. Institut für Informatik, Universität Leipzig, Leipzig, Germany

    Markus Lohrey

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  1. Stefan Göller
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  2. Markus Lohrey
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Correspondence to Markus Lohrey.

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The authors are supported by the DFG research project GELO.

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Göller, S., Lohrey, M. Fixpoint Logics over Hierarchical Structures. Theory Comput Syst 48, 93–131 (2011). https://doi.org/10.1007/s00224-009-9227-1

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