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On the Expressive Power of Hybrid Branching-Time Logics

Authors Daniel Kernberger, Martin Lange

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Daniel Kernberger
  • School of Electrical Engineering and Computer Science, University of Kassel, Germany
Martin Lange
  • School of Electrical Engineering and Computer Science, University of Kassel, Germany

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Daniel Kernberger and Martin Lange. On the Expressive Power of Hybrid Branching-Time Logics. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 16:1-16:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


Hybrid branching-time logics are a powerful extension of branching-time logics like CTL, CTL^* or even the modal mu-calculus through the addition of binders, jumps and variable tests. Their expressiveness is not restricted by bisimulation-invariance anymore. Hence, they do not retain the tree model property, and the finite model property is equally lost. Their satisfiability problems are typically undecidable, their model checking problems (on finite models) are decidable with complexities ranging from polynomial to non-elementary time. In this paper we study the expressive power of such hybrid branching-time logics beyond some earlier results about their invariance under hybrid bisimulations. In particular, we aim to extend the hierarchy of non-hybrid branching-time logics CTL, CTL^+, CTL^* and the modal mu-calculus to their hybrid extensions. We show that most separation results can be transferred to the hybrid world, even though the required techniques become a bit more involved. We also present some collapse results for restricted classes of models that are especially worth investigating, namely linear, tree-shaped and finite models.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • branching-time
  • mu-calculus
  • hybrid logics
  • expressiveness


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