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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.

Cite AsGet BibTex

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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