Progress, Justness and Fairness in Modal $\mu$-Calculus Formulae
<|reference_start|>Progress, Justness and Fairness in Modal $\mu$-Calculus Formulae: 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 $\mu$-calculus. In this paper, we present template formulae in the modal $\mu$-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.<|reference_end|>
@article{spronck2024progress,,
    title={Progress, Justness and Fairness in Modal $\mu$-Calculus Formulae},
    author={Myrthe Spronck, Bas Luttik, Tim Willemse},
    journal={arXiv preprint arXiv:2407.08060},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.08060},
    primaryClass={cs.LO}
}