Formal Methods in System Design

, Volume 40, Issue 3, pp 330–355 | Cite as

A concurrency-preserving translation from time Petri nets to networks of timed automata

Article

Abstract

Several formalisms to model distributed real-time systems coexist in the literature. This naturally induces a need to compare their expressiveness and to translate models from one formalism to another when possible. The first formal comparisons of the expressiveness of these models focused on the preservation of the sequential behavior of the models, using notions like timed language equivalence or timed bisimilarity. They do not consider preservation of concurrency. In this paper we define timed traces as a partial order representation of executions of our models for real-time distributed systems. Timed traces provide an alternative to timed words, and take the distribution of actions into account. We propose a translation between two popular formalisms that describe timed concurrent systems: 1-bounded time Petri nets (TPN) and networks of timed automata (NTA). Our translation preserves the distribution of actions, that is we require that if the TPN represents the product of several components (called processes), then each process should have its counterpart as one timed automaton in the resulting NTA.

Keywords

Concurrency Timed traces Time Petri nets Networks of timed automata Concurrency-preserving translation 

References

  1. 1.
    Akshay S, Bollig B, Gastin P (2007) Automata and logics for timed message sequence charts. In: Foundations of software technology and theoretical computer science (FSTTCS). LNCS, vol 4855. Springer, New Delhi, pp 290–302 Google Scholar
  2. 2.
    Akshay S, Bollig B, Gastin P, Mukund M, Narayan Kumar K (2008) Distributed timed automata with independently evolving clocks. In: International conference on concurrency theory (CONCUR). LNCS, vol 5201. Springer, Toronto, pp 82–97 Google Scholar
  3. 3.
    Alur R, Dill DL (1994) A theory of timed automata. Theor Comput Sci 126(2):183–235 MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Balaguer S, Chatain Th, Haar S (2010) A concurrency-preserving translation from time Petri nets to networks of timed automata. In: International symposium on temporal representation and reasoning (TIME). IEEE Computer Society Press, Paris, pp 77–84 CrossRefGoogle Scholar
  5. 5.
    Bérard B, Cassez F, Haddad S, Lime D, Roux OH (2008) When are timed automata weakly timed bisimilar to time Petri nets? Theor Comput Sci 403(2–3):202–220 MATHCrossRefGoogle Scholar
  6. 6.
    Berthomieu B, Diaz M (1991) Modeling and verification of time dependent systems using time Petri nets. IEEE Trans Softw Eng 17(3):259–273 MathSciNetCrossRefGoogle Scholar
  7. 7.
    Berthomieu B, Ribet PO, Vernadat F (2004) The tool TINA—construction of abstract state spaces for Petri nets and time Petri nets. Int J Prod Res 42(14):2741–2756 MATHCrossRefGoogle Scholar
  8. 8.
    Bozga M, Daws C, Maler O, Olivero A, Tripakis S, Yovine S (1998) Kronos: a model-checking tool for real-time systems. In: International conference on computer aided verification (CAV). LNCS, vol 1427, pp 546–550 CrossRefGoogle Scholar
  9. 9.
    Byg J, Joergensen K, Srba J (2009) An efficient translation of timed-arc Petri nets to networks of timed automata. In: International conference on formal engineering methods. LNCS, vol 5885. Springer, Berlin, pp 698–716 Google Scholar
  10. 10.
    Cassez F, Roux OH (2006) Structural translation from time Petri nets to timed automata. J Syst Softw Google Scholar
  11. 11.
    Cerans K, Godskesen JC, Larsen KG (1993) Timed modal specification—theory and tools. In: International conference on computer aided verification (CAV). LNCS, vol 697. Springer, Berlin, pp 253–267 CrossRefGoogle Scholar
  12. 12.
    Colom JM, Silva M (1991) Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal p-semiflows. In: Proceedings of the 10th international conference on applications and theory of Petri nets. Springer, London, pp 79–112 Google Scholar
  13. 13.
    Desel J, Esparza J (1995) Free choice Petri nets. Cambridge University Press, New York MATHCrossRefGoogle Scholar
  14. 14.
    Diekert V, Rozenberg G (1995) The book of traces. World Scientific Publishing Co, Inc, River Edge CrossRefGoogle Scholar
  15. 15.
    Gardey G, Lime D, Magnin M, Roux OH (2005) Romeo: A tool for analyzing time Petri nets. In: International conference on computer aided verification (CAV). LNCS, vol 3576. Springer, Berlin, pp 418–423 CrossRefGoogle Scholar
  16. 16.
    Gardey G, Roux OH, Roux OF (2006) State space computation and analysis of time Petri nets. Theory Pract Log Program 6(3):301–320 MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Hack M (1972) Analysis of production schemata by Petri nets. Master’s thesis, Massachusetts Institute of Technology, Cambridge, USA Google Scholar
  18. 18.
    Henzinger TA, Kopke PW, Wong-Toi H (1995) The expressive power of clocks. In: International colloquium on automata, languages and programming (ICALP), pp 417–428 CrossRefGoogle Scholar
  19. 19.
    Jensen K, Kristensen LM, Wells L (2007) Coloured Petri nets and cpn tools for modelling and validation of concurrent systems. Int J Softw Tools Technol Transf 9(3–4):213–254 CrossRefGoogle Scholar
  20. 20.
    Lanotte R, Maggiolo-Schettini A, Peron A (2000) Timed cooperating automata. Fundam Inform 43:153–173 MathSciNetMATHGoogle Scholar
  21. 21.
    Larsen KG, Pettersson P, Yi W (1997) Uppaal in a nutshell. Int J Softw Tools Technol Transf 1(1–2):134–152 MATHGoogle Scholar
  22. 22.
    Lautenbach K (1975) Liveness in Petri nets. Tech rep, Gesellschaft für Mathematik und Datenverarbeitung, Bonn, Germany Google Scholar
  23. 23.
    Lime D, Roux OH (2006) Model checking of time Petri nets using the state class timed automaton. J Discrete Event Dyn Syst 16(2):179–205 MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Lugiez D, Niebert P, Zennou S (2005) A partial order semantics approach to the clock explosion problem of timed automata. Theor Comput Sci 345(1):27–59 MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Merlin PM (1974) A study of the recoverability of computing systems. PhD thesis, University of California, Irvine Google Scholar
  26. 26.
    Niebert P, Qu H (2006) Adding invariants to event zone automata. In: International conference on formal modelling and analysis of timed systems (FORMATS). LNCS, vol 4202. Springer, Berlin, pp 290–305 CrossRefGoogle Scholar
  27. 27.
    Sifakis J, Yovine S (1996) Compositional specification of timed systems (extended abstract). In: Symposium on theoretical aspects of computer science (STACS). Springer, London, pp 347–359 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.INRIA, LSVENS Cachan, CNRSCachanFrance

Personalised recommendations