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Bandwidth of Timed Automata: 3 Classes

Authors Eugene Asarin , Aldric Degorre , Cătălin Dima , Bernardo Jacobo Inclán

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Author Details

Eugene Asarin
  • Université Paris Cité, CNRS, IRIF, Paris, France
Aldric Degorre
  • Université Paris Cité, CNRS, IRIF, Paris, France
Cătălin Dima
  • LACL, Université Paris-Est Créteil, France
Bernardo Jacobo Inclán
  • Université Paris Cité, CNRS, IRIF, Paris, France

Funding

This work was supported by the ANR project MAVeriQ ANR-CE25-0012 and by the ANR-JST project CyPhAI.

Acknowledgements

We thank the anonymous reviewers for their careful reading and valuable comments which helped to improve the paper.

Cite AsGet BibTex

Eugene Asarin, Aldric Degorre, Cătălin Dima, and Bernardo Jacobo Inclán. Bandwidth of Timed Automata: 3 Classes. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSTTCS.2023.10

Abstract

Timed languages contain sequences of discrete events ("letters") separated by real-valued delays, they can be recognized by timed automata, and represent behaviors of various real-time systems. The notion of bandwidth of a timed language defined in [Jacobo Inclán et al., 2022] characterizes the amount of information per time unit, encoded in words of the language observed with some precision ε. In this paper, we identify three classes of timed automata according to the asymptotics of the bandwidth of their languages with respect to this precision ε: automata are either meager, with an O(1) bandwidth, normal, with a Θ(log(1/ε)) bandwidth, or obese, with Θ(1/ε) bandwidth. We define two structural criteria and prove that they partition timed automata into these 3 classes of bandwidth, implying that there are no intermediate asymptotic classes. The classification problem of a timed automaton is PSPACE-complete. Both criteria are formulated using morphisms from paths of the timed automaton to some finite monoids extending Puri’s orbit graphs; the proofs are based on Simon’s factorization forest theorem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantitative automata
  • Theory of computation → Timed and hybrid models
Keywords
  • timed automata
  • information theory
  • bandwidth
  • entropy
  • orbit graphs
  • factorization forests

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