Formal Methods in System Design

, Volume 45, Issue 3, pp 330–380 | Cite as

On regions and zones for event-clock automata

  • Gilles Geeraerts
  • Jean-François Raskin
  • Nathalie Sznajder
Article

Abstract

Event clock automata (\(\mathsf{ECA}\) ) are a model for timed languages that has been introduced by Alur, Fix and Henzinger as an alternative to timed automata, with better theoretical properties (for instance, \(\mathsf{ECA}\)   are determinizable while timed automata are not). In this paper, we revisit and extend the theory of \(\mathsf{ECA}\) . We first prove that no finite time abstract language equivalence exists for \(\mathsf{ECA}\) , thereby disproving a claim in the original work on \(\mathsf{ECA}\) . This means in particular that regions do not form a time abstract bisimulation. Nevertheless, we show that regions can still be used to build a finite automaton recognizing the untimed language of an\(\mathsf{ECA}\) . Then, we extend the classical notions of zones and DBMs to let them handle event clocks instead of plain clocks (as in timed automata) by introducing event zones and Event DBMs (EDBMs). We discuss algorithms to handle event zones represented as EDBMs, as well as (semi-) algorithms based on EDBMs to decide language emptiness of \(\mathsf{ECA}\) .

Keywords

Event clock automata Timed automata Real-time Verification Formal methods Zones regions DBMs 

References

  1. 1.
    Alur R (1999) Timed automata. In: Proceedings of CAV’99, vol 1633. Lecture notes in computer science. Springer, Berlin, pp 8–22Google Scholar
  2. 2.
    Alur R, Courcoubetis C, Dill D (1993) Model-checking in dense real-time. Inf Comput 104:2–34CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Alur R, Dill D (1994) A theory of timed automata. Theor Comput Sci 126(2):183–236CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Alur R, Fix L, Henzinger TA (1999) Event-clock automata: a determinizable class of timed automata. Theor Comput Sci 211(1–2):253–273CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Behrmann G, David A, Larsen KG, Håkansson J, Pettersson P, Yi W, Hendriks M (2006) Uppaal 4.0. In: Proceedings of QEST’06. IEEE Computer Society, New York, pp 125–126Google Scholar
  6. 6.
    Bellman R (1957) Dynamic programming. Princeton university press, PrincetonMATHGoogle Scholar
  7. 7.
    Bengtsson J, Griffioen WOD, Kristoffersen KJ, Larsen KG, Larsson F, Pettersson P, Yi W (2002) Automated verification of an audio-control protocol using Uppaal. J Log Algebr Program 52–53:163–181Google Scholar
  8. 8.
    Bouyer P (2002) Modèles et algorithmes pour la vérification des systèmes temporisés. Thèse de doctorat, Laboratoire Spécification et Vérification. ENS Cachan, FranceGoogle Scholar
  9. 9.
    Bouyer P (2002) Timed automata may cause some troubles. In Research Report LSV-02-9, LSV, ENS DE CACHAN. http://www.lsv.enscachan.fr/Publis/RAPPORTS_LSV/PS/rrlsv-2002-9.rr.ps
  10. 10.
    Bouyer P (2004) Forward analysis of updatable timed automata. Formal Methods Syst Des 24(3):281–320CrossRefMATHGoogle Scholar
  11. 11.
    Bouyer P, Laroussinie F, Reynier P-A (2005) Diagonal constraints in timed automata: Forward analysis of timed systems. In: Pettersson P, Yi W (eds) Formal modeling and analysis of timed systems, vol 3829. Lecture notes in computer science. Springer, Berlin, pp 112–126Google Scholar
  12. 12.
    Bozga M, Daws C, Maler O, Olivero A, Tripakis S, Yovine S (1998) Kronos: A model-checking tool for real-time systems. In: Proceedings of CAV’98, vol 1427. Lecture notes in computer science. Springer, Berlin, pp 546–550Google Scholar
  13. 13.
    Cerans K (1993) Decidability of bisimulation equivalences for parallel timer processes. In: Proceedings of the fourth international workshop on computer aided verification, CAV ’92, London. Springer, Berlin, pp 302–315Google Scholar
  14. 14.
    Daws C, Tripakis S (1998) Model checking of real-time reachability properties using abstractions. In Steffen B (ed) Proceedings of TACAS’98, vol 1384. Lecture notes in computer science. Springer, Berlin, pp 313–329Google Scholar
  15. 15.
    Daws C, Tripakis S (1998) Model checking of real-time reachability properties using abstractions. In: TACAS. Springer, Berlin, pp 313–329Google Scholar
  16. 16.
    Di Giampaolo B, Geeraerts G, Raskin J, Sznajder N (2010) Safraless procedures for timed specifications. In: Proceedings of FORMATS’10, vol 6246. Lecture notes in computer science. Springer, Berlin, pp 2–22Google Scholar
  17. 17.
    Diekert V, Gastin P, Petit A (1997) Removing epsilon-transitions in timed automata. In: STACS 97, 14th Annual Symposium on theoretical aspects of computer science, vol 1200. Lecture notes in computer science. Springer, Berlin, pp 583–594Google Scholar
  18. 18.
    Dill DL (1989) Timing assumptions and verification of finite-state concurrent systems. In: Proceedings of automatic verification methods for finite state systems, vol 407. Lecture notes in computer science. Springer, Berlin, pp 197–212Google Scholar
  19. 19.
    Dima C (1999) Kleene theorems for event-clock automata. In: Proceedings of FCT’99, volume 1684 of Lecture Notes in computer science. Springer, Berlin, pp 215–225Google Scholar
  20. 20.
    D’Souza D, Tabareau N (2004) On timed automata with input-determined guards. In Proccedings of FORMATS/FTRTFT’04, vol 3253. Lecture notes in computer science. Springer, Berlin, pp 68–83Google Scholar
  21. 21.
    Geeraerts G, Raskin J-F, Sznajder N (2011) Event-clock automata : from theory to practice. In: Fahrenberg U, Tripakis S (eds) Proceedings of the 9th international conference on formal modelling and analysis of timed systems (FORMATS’11), vol 6919. Lecture notes in computer science. Springer, Berlin, pp 209–224Google Scholar
  22. 22.
    Lindahl M, Pettersson P, Yi W (1998) Formal design and analysis of a gear-box controller. In: Proceedings of the 4th workshop on tools and algorithms for the construction and analysis of systems. vol 1384 .Lecture notes in computer science. Springer, Berlin, pp 281–297Google Scholar
  23. 23.
    Miné A (2006) The octagon abstract domain. Higher-Order Symbol Comput 19(1):31–100, 2006. http://www.di.ens.fr/~mine/publi/article-mine-HOSC06.pdf
  24. 24.
    Pettersson, P, Yi W editors. Formal Modeling and Analysis of Timed Systems. In: Proceedings of the third international conference, FORMATS 2005, Uppsala, September 26–28, 2005, vol 3829. Lecture notes in computer science. Springer, BerlinGoogle Scholar
  25. 25.
    Raskin J-F, Schobbens P-Y (1998) The logic of event clocks: decidability, complexity and expressiveness. Automatica 34(3):247–282MathSciNetGoogle Scholar
  26. 26.
    Sorea M (2001) Tempo: a model-checker for event-recording automata. In: Proceedings of RT-TOOLS’01, AalborgGoogle Scholar
  27. 27.
    Tang N, Ogawa M (2009) Event-clock visibly pushdown automata. In: Proceedings of SOFSEM’09, vol 5404. Lecture notes in computer science. Springer, Berlin, pp 558–569Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Gilles Geeraerts
    • 1
  • Jean-François Raskin
    • 1
  • Nathalie Sznajder
    • 2
  1. 1.Faculté des Sciences, Département d’InformatiqueUniversité libre de BruxellesBrusselsBelgium
  2. 2.Sorbonne UniversitésParisFrance

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