The Tail-Recursive Fragment of Timed Recursive CTL

Authors Florian Bruse, Martin Lange, Etienne Lozes

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Author Details

Florian Bruse
  • School of Electrical Engineering and Computer Science, Universität Kassel, Germany
Martin Lange
  • School of Electrical Engineering and Computer Science, Universität Kassel, Germany
Etienne Lozes
  • Laboratoire d’Informatique, Signaux et Systèmes de Sophia-Antipolis, Université Côte d'Azur, France

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Florian Bruse, Martin Lange, and Etienne Lozes. The Tail-Recursive Fragment of Timed Recursive CTL. In 29th International Symposium on Temporal Representation and Reasoning (TIME 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 247, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Timed Recursive CTL (TRCTL) was recently proposed as a merger of two extensions of the well-known branching-time logic CTL: Timed CTL on one hand is interpreted over real-time systems like timed automata, and Recursive CTL (RecCTL) on the other hand obtains high expressiveness through the introduction of a recursion operator. Model checking for the resulting logic is known to be 2-EXPTIME-complete. The aim of this paper is to investigate the possibility to obtain a fragment of lower complexity without losing too much expressive power. It is obtained by a syntactic property called "tail-recursiveness" that restricts the way that recursive formulas can be built. This restriction is known to decrease the complexity of model checking by half an exponential in the untimed setting. We show that this also works in the real-time world: model checking for the tail-recursive fragment of TRCTL is EXPSPACE-complete. The upper bound is obtained by a standard untiming construction via region graphs, and rests on the known complexity of tail-recursive fragments of higher-order modal logics. The lower bound is established by a reduction from a suitable tiling problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Program specifications
  • formal specification
  • temporal logic
  • real-time systems


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