Thin and Thick Timed Regular Languages View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2011

AUTHORS

Nicolas Basset , Eugene Asarin

ABSTRACT

In previous literature on timed automata, it was noticed that they are in several aspects too precise, which leads sometimes to strange artifacts, mathematical pathologies or unrealistic models. In particular, some timed automata are non-implementable, non-robust, behave badly under discretization, have many Zeno runs etc. In this paper, we propose a unifying approach to most of these issues for deterministic timed automata. We classify these automata either as thin or as thick. In thin automata, all the infinite trajectories are, in some weak sense, Zeno; the discretization of long trajectories is difficult, since it requires very small discretization step. In thick automata, most of trajectories are non-Zeno and behave well under discretization; such automata satisfy a sort of pumping lemma. Formally, the thin-thick alternative is based on the notion of entropy of timed regular languages introduced by E. Asarin and A. Degorre in [3,4]. Thin languages have the entropy = − ∞ while thick have a larger one. An important application of thin-thick alternative is again the entropy theory of timed languages. We show that the entropy can be computed with a desired precision using discretization and thus it is computable, which closes a question left open in [3,4]. More... »

PAGES

113-128

References to SciGraph publications

  • 1998. Pumping Lemmas for timed automata in FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES
  • 2000-12. Mean topological dimension in ISRAEL JOURNAL OF MATHEMATICS
  • 2009. Volume and Entropy of Regular Timed Languages: Discretization Approach in CONCUR 2009 - CONCURRENCY THEORY
  • 2002-04-19. Timed Automata and the Theory of Real Numbers in CONCUR’99 CONCURRENCY THEORY
  • 2007. Efficient Detection of Zeno Runs in Timed Automata in FORMAL MODELING AND ANALYSIS OF TIMED SYSTEMS
  • 2000. Robust Undecidability of Timed and Hybrid Systems in HYBRID SYSTEMS: COMPUTATION AND CONTROL
  • 1992. What good are digital clocks? in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 1998. On discretization of delays in timed automata and digital circuits in CONCUR'98 CONCURRENCY THEORY
  • 2008-12. Robust safety of timed automata in FORMAL METHODS IN SYSTEM DESIGN
  • 2000-01. Dynamical Properties of Timed Automata in DISCRETE EVENT DYNAMIC SYSTEMS
  • 1997. Robust timed automata in HYBRID AND REAL-TIME SYSTEMS
  • 2005-10. Almost ASAP semantics: from timed models to timed implementations in FORMAL ASPECTS OF COMPUTING
  • 2004. On Recognizable Timed Languages in FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES
  • 2009. Volume and Entropy of Regular Timed Languages: Analytic Approach in FORMAL MODELING AND ANALYSIS OF TIMED SYSTEMS
  • Book

    TITLE

    Formal Modeling and Analysis of Timed Systems

    ISBN

    978-3-642-24309-7
    978-3-642-24310-3

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-24310-3_9

    DOI

    http://dx.doi.org/10.1007/978-3-642-24310-3_9

    DIMENSIONS

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