Progress, Justness and Fairness in Modal μ-Calculus Formulae
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Progress, Justness and Fairness in Modal μ-Calculus Formulae

Authors Myrthe S. C. Spronck , Bas Luttik , Tim A. C. Willemse

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Myrthe S. C. Spronck
  • Eindhoven University of Technology, The Netherlands
Bas Luttik
  • Eindhoven University of Technology, The Netherlands
Tim A. C. Willemse
  • Eindhoven University of Technology, The Netherlands

Acknowledgements

We thank an anonymous reviewer for the observation that weak and strong hyperfairness must be distinguished.

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Myrthe S. C. Spronck, Bas Luttik, and Tim A. C. Willemse. Progress, Justness and Fairness in Modal μ-Calculus Formulae. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 38:1-38:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.38

Abstract

When verifying liveness properties on a transition system, it is often necessary to discard spurious violating paths by making assumptions on which paths represent realistic executions. Capturing that some property holds under such an assumption in a logical formula is challenging and error-prone, particularly in the modal μ-calculus. In this paper, we present template formulae in the modal μ-calculus that can be instantiated to a broad range of liveness properties. We consider the following assumptions: progress, justness, weak fairness, strong fairness, and hyperfairness, each with respect to actions. The correctness of these formulae has been proven.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • Modal μ-calculus
  • Property specification
  • Completeness criteria
  • Progress
  • Justness
  • Fairness
  • Liveness properties

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