Skip to main content
SpringerLink
Log in

Thin and Thick Timed Regular Languages

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6919))

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].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdulla, P.A., Krcál, P., Yi, W.: Sampled semantics of timed automata. Logical Methods in Computer Science 6(3) (2010)

    Google Scholar 

  2. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Asarin, E., Degorre, A.: Volume and entropy of regular timed languages: Analytic approach. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 13–27. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Asarin, E., Degorre, A.: Volume and entropy of regular timed languages: Discretization approach. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 69–83. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Asarin, E., Degorre, A.: Two size measures for timed languages. In: FSTTCS, Schloss Dagstuhl - Leibniz-Zentrum für Informatik. LIPIcs, vol. 8, pp. 376–387 (2010)

    Google Scholar 

  6. Asarin, E., Maler, O., Pnueli, A.: On discretization of delays in timed automata and digital circuits. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 470–484. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  7. Beauquier, D.: Pumping lemmas for timed automata. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 81–94. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Beck, M., Robins, S.: Computing the continuous discretely: Integer-point enumeration in polyhedra. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  9. Carnevali, L., Grassi, L., Vicario, E.: State-density functions over DBM domains in the analysis of non-Markovian models. IEEE Trans. Software Eng. 35(2), 178–194 (2009)

    Article  Google Scholar 

  10. Comon, H., Jurski, Y.: Timed automata and the theory of real numbers. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 242–257. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Dima, C.: Computing reachability relations in timed automata. In: LICS, p. 177. IEEE Computer Society, Los Alamitos (2002)

    Google Scholar 

  12. Gómez, R., Bowman, H.: Efficient detection of Zeno runs in timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 195–210. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Gupta, V., Henzinger, T.A., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 331–345. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  14. Henzinger, T.A., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 545–558. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  15. Henzinger, T.A., Raskin, J.F.: Robust undecidability of timed and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 145–159. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  16. Krcál, P.: Infinite Structures in Timed Systems. Ph.D. thesis, University of Uppsala, Dept. of Information Technology (May 2009)

    Google Scholar 

  17. Lindenstrauss, E., Weiss, B.: Mean topological dimension. Israel J. Math 115, 1–24 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Maler, O., Pnueli, A.: On recognizable timed languages. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 348–362. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. Puri, A.: Dynamical properties of timed automata. Discrete Event Dynamic Systems 10(1-2), 87–113 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Simon, I.: Factorization forests of finite height. Theor. Comput. Sci. 72(1), 65–94 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wulf, M.D., Doyen, L., Markey, N., Raskin, J.F.: Robust safety of timed automata. Formal Methods in System Design 33(1-3), 45–84 (2008)

    Article  MATH  Google Scholar 

  22. Wulf, M.D., Doyen, L., Raskin, J.F.: Almost ASAP semantics: from timed models to timed implementations. Formal Asp. Comput. 17(3), 319–341 (2005)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIGM, Université Paris-Est and CNRS, France

    Nicolas Basset

  2. LIAFA, Université Paris Diderot and CNRS, France

    Eugene Asarin

Authors
  1. Nicolas Basset
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eugene Asarin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IRISA/INRIA Rennes, Campus Beaulieu, 35042, Rennes Cedex, France

    Uli Fahrenberg

  2. University of California, 94720-1770, Berkeley, CA, USA

    Stavros Tripakis

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Basset, N., Asarin, E. (2011). Thin and Thick Timed Regular Languages. In: Fahrenberg, U., Tripakis, S. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2011. Lecture Notes in Computer Science, vol 6919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24310-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24310-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24309-7

  • Online ISBN: 978-3-642-24310-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation