Discrete Event Dynamic Systems

, 21:395 | Cite as

On the composition of time Petri nets

  • Florent Peres
  • Bernard Berthomieu
  • François Vernadat


Complex systems are often designed and built from smaller pieces, called components. Components are open sub-systems meant to be combined (or composed) to form other components or closed systems. It is well known that Petri nets allow such a component based modeling, relying on parallel composition and transition synchronization. However, synchronizing transitions that carry temporal constraints does not yield a compositional method for assembling components, a highly desirable property. The paper addresses this particular problem: how to build complex systems in a compositional manner from components specified by Time Petri nets (TPN). A first solution is proposed, adequate for a particular subclass of Time Petri nets but significantly increasing the complexity of components. Then an improved solution is developed, relying on an extension of Time Petri nets with two relations added on transitions. This latter solution requires a much simpler transformation of nets, does not significantly increase their complexity, and is applicable to a larger class of TPN.


Composition Time Petri nets Compositionality 


  1. Bérard B, Cassez F, Haddad S, Roux OH, Lime D (2005a) Comparison of the expressiveness of timed automata and time Petri nets. In: Formal modeling and analysis of timed systems (FORMATS). LNCS 3829, pp 211–225Google Scholar
  2. Bérard B, Cassez F, Haddad S, Roux OH, Lime D (2005b) When are timed automata weakly timed bisimilar to time Petri nets? In: 25th conference on foundations of software technology and theoretical computer science. LNCS 3821. Springer, pp 261–272Google Scholar
  3. Berthomieu B, Menasche M (1983) An enumerative approach for analyzing time Petri nets. IFIP Congr Ser 9:41–46Google Scholar
  4. Berthomieu B, Vernadat F (2003) State class constructions for branching analysis of time Petri nets. In: Proc. tools and algorithms for the construction and analysis of systems. LNCS 2619. SpringerGoogle Scholar
  5. Berthomieu B, Ribet P-O, Vernadat F (2003) L’outil Tina—construction d’espaces d’etats abstraits pour les réseaux de Petri et réseaux temporels. In: Proc. Modélisation des Systèmes Réactifs, Metz, FranceGoogle Scholar
  6. Berthomieu B, Ribet P-O, Vernadat F (2004) The tool TINA—construction of abstract state spaces for Petri nets and time Petri nets. Int J Prod Res 42(14):2741–2756zbMATHCrossRefGoogle Scholar
  7. Berthomieu B, Peres F, Vernadat F (2006) Bridging the gap between timed automata and bounded time Petri nets. In: 4th int. conf. on formal modelling and analysis of timed systems (FORMATS). LNCS 4202. SpringerGoogle Scholar
  8. Boyer M, Roux O (2007) Comparison of the expressiveness of arc, place and transition time Petri nets. In: Kleijn J, Yakovlev A (eds) Petri nets and other models of concurrency—ICATPN 2007. Lecture notes in computer science, vol 4546. Springer Berlin/Heidelberg, pp 63–82CrossRefGoogle Scholar
  9. Bouyer P, Haddad S, Reynier P-A (2006) Extended timed automata and time Petri nets. In: Proc. of 6th international conference on application of concurrency to system design (ACSD’06), Turku, Finland. IEEE Computer Society PressGoogle Scholar
  10. Browne MC, Clarke EM, Grümberg O (1988) Characterizing finite Kripke structures in propositional temporal logics. TCS 59:115–131zbMATHCrossRefGoogle Scholar
  11. Bucci G, Vicario E (1995) Compositional validation of time-critical systems using communicating time Petri nets. IEEE Trans Softw Eng 21(12):969–992CrossRefGoogle Scholar
  12. Cassez F, Roux OH (2006) Structural translation from time Petri nets to timed automata. J Syst Softw 29(1):1456–1468CrossRefGoogle Scholar
  13. Gardey G, Lime D, Magnin M, Roux OH (2005) Roméo: a tool for analyzing time Petri nets. In: 17th international conference on computer aided verification, CAV’05. LNCS 3576. SpringerGoogle Scholar
  14. Gössler G, Sifakis J (2003) Composition for components-based modeling. In: Formal methods for components and objects. LNCS 2852. Springer, pp 443–466Google Scholar
  15. Hack M (1976) Petri net languages. Technical Report 159. MIT, Cambridge, MAGoogle Scholar
  16. Larsen KG, Pettersson P, Yi WY (1995) Model-checking for real-time systems. In: Fundamentals of computation theory. LNCS 965, pp 62–88Google Scholar
  17. Merlin PM, Farber DJ (1976) Recoverability of communication protocols: implications of a theoretical study. IEEE Trans Commun 24(9):1036–1043zbMATHCrossRefMathSciNetGoogle Scholar
  18. Peres F (2010) Réseaux de Petri temporels à inhibitions/permissions—application à la modélisation de systèmes de tâches temps réel. Thèse de l’Université de Toulouse, JanvierGoogle Scholar
  19. Peres F, Berthomieu B, Vernadat F (2009) Composer les réseaux de Petri temporels. Journal Europeen des Systemes Automatises 43(7–9):1001–1015. CrossRefGoogle Scholar
  20. Sifakis J, Yovine S (1996) Compositional specification of timed systems. In: 13th annual symp. on theoretical aspects of computer science (STACS). LNCS 1046, Springer, pp 347–359Google Scholar
  21. van Glabbeek R (1990) The linear time—branching time spectrum. In: Baeten J, Klop J (eds) CONCUR ’90 theories of concurrency: unification and extension. Lecture notes in computer science, vol 458. Springer Berlin/HeidelbergGoogle Scholar
  22. Wang Y (1990) Real-time behaviour of asynchronous agents. In: Baeten J, Klop J (eds) CONCUR ’90 theories of concurrency: unification and extension. Lecture notes in computer science, vol 458. Springer Berlin/Heidelberg, pp 502–520CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Florent Peres
    • 1
    • 2
  • Bernard Berthomieu
    • 3
    • 4
  • François Vernadat
    • 3
    • 4
  1. 1.Université Lille Nord de FranceLilleFrance
  2. 2.IFSTTAR, ESTASVilleneuve d’AscqFrance
  3. 3.CNRS; LAASToulouseFrance
  4. 4.Université de Toulouse; UPS, INSA, INP, INSAE; LAASToulouseFrance

Personalised recommendations