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The mu-calculus and Model Checking

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Abstract

This chapter presents that part of the theory of the \(\mu\)-calculus that is relevant to the model-checking problem as broadly understood. The \(\mu\)-calculus is one of the most important logics in model checking. It is a logic with an exceptional balance between expressiveness and algorithmic properties.

The chapter describes at length the game characterization of the semantics of the \(\mu\)-calculus. It discusses the theory of the \(\mu\)-calculus starting with the tree-model property, and bisimulation invariance. Then it develops the notion of modal automaton: an automaton-based model behind the \(\mu\)-calculus. It gives a quite detailed explanation of the satisfiability algorithm, followed by results on alternation hierarchy, proof systems, and interpolation. Finally, the chapter discusses the relation of the \(\mu\)-calculus to monadic second-order logic as well as to some program and temporal logics. It also presents two extensions of the \(\mu\)-calculus that allow us to address issues such as inverse modalities.

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Authors and Affiliations

  1. University of Edinburgh, Edinburgh, UK

    Julian Bradfield

  2. CNRS, University of Bordeaux, Bordeaux, France

    Igor Walukiewicz

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  1. Julian Bradfield
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  2. Igor Walukiewicz
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Correspondence to Igor Walukiewicz .

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Editors and Affiliations

  1. FORE Systems University Professor of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Edmund M. Clarke

  2. Institute of Science and Technology Austria (IST), Klosterneuburg, Austria

    Thomas A. Henzinger

  3. Arbeitsbereich Formal Methods in Systems Engineering, Technische Universität Wien, Wien, Austria

    Helmut Veith

  4. Institut f. Angewandte Informationsverarbeitung und Kommunikationstechnologie (IAIK), Technische Universität Graz, Graz, Austria

    Roderick Bloem

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Bradfield, J., Walukiewicz, I. (2018). The mu-calculus and Model Checking. In: Clarke, E., Henzinger, T., Veith, H., Bloem, R. (eds) Handbook of Model Checking. Springer, Cham. https://doi.org/10.1007/978-3-319-10575-8_26

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  • DOI: https://doi.org/10.1007/978-3-319-10575-8_26

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