The Fully Hybrid mu-Calculus

Authors Daniel Kernberger, Martin Lange

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Daniel Kernberger
Martin Lange

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Daniel Kernberger and Martin Lange. The Fully Hybrid mu-Calculus. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We consider the hybridisation of the mu-calculus through the addition of nominals, binder and jump. Especially the use of the binder differentiates our approach from earlier hybridisations of the mu-calculus and also results in a more involved formal semantics. We then investigate the model checking problem and obtain ExpTime-completeness for the full logic and the same complexity as the modal mu-calculus for a fixed number of variables. We also show that this logic is invariant under hybrid bisimulation and use this result to show that - contrary to the non-hybrid case - the hybrid extension of the full branching time logic CTL* is not a fragment of the fully hybrid mu-calculus.
  • mu-calculus
  • hybrid logics
  • model checking
  • bisimulation invariance


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