Verification of Timed-Arc Petri Nets

  • Lasse Jacobsen
  • Morten Jacobsen
  • Mikael H. Møller
  • Jiří Srba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6543)


Timed-Arc Petri Nets (TAPN) are an extension of the classical P/T nets with continuous time. Tokens in TAPN carry an age and arcs between places and transitions are labelled with time intervals restricting the age of tokens available for transition firing. The TAPN model posses a number of interesting theoretical properties distinguishing them from other time extensions of Petri nets. We shall give an overview of the recent theory developed in the verification of TAPN extended with features like read/transport arcs, timed inhibitor arcs and age invariants. We will examine in detail the boundaries of automatic verification and the connections between TAPN and the model of timed automata. Finally, we will mention the tool TAPAAL that supports modelling, simulation and verification of TAPN and discuss a small case study of alternating bit protocol.


Atomic Proposition Input Place Time Automaton Small Case Study UPPAAL Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
  2. 2.
  3. 3.
    Abdulla, P.A., Nylén, A.: Better is better than well: On efficient verification of infinite-state systems. In: Proceedings of 15th Annual IEEE Symposium on Logic in Computer Science (LICS 2000), pp. 132–140 (2000)Google Scholar
  4. 4.
    Abdulla, P.A., Nylén, A.: Timed Petri nets and BQOs. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 53–70. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Abdulla, P.A., Deneux, J., Mahata, P., Nylén, A.: Forward reachability analysis of timed Petri nets. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 343–362. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Abdulla, P.A., Mahata, P., Mayr, R.: Dense-timed Petri nets: Checking zenoness, token liveness and boundedness. Logical Methods in Computer Science 3(1), 1–61 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Alur, R., Dill, D.: Automata for modelling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  8. 8.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Bartlett, K.A., Scantlebury, R.A., Wilkinson, P.T.: A note on reliable full-duplex transmission over half-duplex links. Communications of the ACM 12(5), 260–261 (1969)CrossRefGoogle Scholar
  10. 10.
    Behrmann, G., David, A., Larsen, K.G.: A tutorial on uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Software Eng. 17(3), 259–273 (1991)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Berthomieu, B., Ribet, P.-O., Vernadat, F.: The tool TINA — construction of abstract state spaces for Petri nets and time Petri nets. International Journal of Production Research 42(14), 2741–2756 (2004)CrossRefzbMATHGoogle Scholar
  13. 13.
    Berthomieu, B., Peres, F., Vernadat, F.: Bridging the gap between timed automata and bounded time Petri nets. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 82–97. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Bolognesi, T., Cremonese, P.: The weakness of some timed models for concurrent systems. Technical Report CNUCE C89-29, CNUCE–C.N.R (1989)Google Scholar
  15. 15.
    Bolognesi, T., Lucidi, F., Trigila, S.: From timed Petri nets to timed LOTOS. In: Proceedings of the IFIP WG 6.1 Tenth International Symposium on Protocol Specification, Testing and Verification (Ottawa 1990), pp. 1–14. North-Holland, Amsterdam (1990)Google Scholar
  16. 16.
    Boucheneb, H., Gardey, G., Roux, O.H.: TCTL model checking of time Petri nets. Journal of Logic and Computation 19(6), 1509–1540 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Bouyer, P., Haddad, S., Reynier, P.-A.: Timed Petri nets and timed automata: On the discriminating power of zeno sequences. Information and Computation 206(1), 73–107 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Bouyer, P., Haddad, S., Reynier, P.A.: Timed Petri nets and timed automata: On the discriminating power of Zeno sequences. Information and Computation 206(1), 73–107 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Bowden, F.D.J.: Modelling time in Petri nets. In: Proceedings of the Second Australia-Japan Workshop on Stochastic Models (1996)Google Scholar
  20. 20.
    Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  21. 21.
    Bozga, M., Graf, S., Ober, I., Ober, I., Sifakis, J.: The IF toolset. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 237–267. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Byg, J., Jørgensen, K.Y., Srba, J.: An efficient translation of timed-arc Petri nets to networks of timed automata. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 698–716. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Byg, J., Jørgensen, K.Y., Srba, J.: TAPAAL: Editor, simulator and verifier of timed-arc Petri nets. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 84–89. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Cassez, F., Roux, O.H.: Structural translation from time Petri nets to timed automata. ENTCS 128(6), 145 (2005); Proc. of AVoCS 2004 (2004)zbMATHGoogle Scholar
  25. 25.
    Dong, J.S., Hao, P., Qin, S., Sun, J., Yi, W.: Timed Automata Patterns. IEEE Transactions on Software Engingeering 34(6), 844–859 (2008)CrossRefGoogle Scholar
  26. 26.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256(1-2), 63–92 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Gardey, G., Lime, D., Magnin, M., Roux, O.H.: Romeo: A tool for analyzing time Petri nets. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 418–423. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  28. 28.
    Hack, M.: Petri Net Language. Technical Report MIT-LCS-TR-159, Massachusetts Institute of Technology, Cambridge, MA, USA (1976)Google Scholar
  29. 29.
    Hanisch, H.M.: Analysis of place/transition nets with timed-arcs and its application to batch process control. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 282–299. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  30. 30.
    Heitmann, F., Moldt, D., Mortensen, K.H., Rölke, H.: Petri nets tools database quick overview, (accessed: 28.10.2010)
  31. 31.
    Jacobsen, L., Jacobsen, M., Møller, M.H.: Undecidability of coverability and boundedness for timed-arc Petri nets with invariants. In: Proc. of MEMICS 2009. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2009) ISBN 978-3-939897-15-6Google Scholar
  32. 32.
    Jacobsen, L., Jacobsen, M., Møller, M.H.: Modelling and verification of timed-arc Petri nets. Master’s thesis, Department of Computer Science, Aalborg University, Denmark (2010a), http://tapaal.netGoogle Scholar
  33. 33.
    Jacobsen, L., Jacobsen, M., Møller, M.H., Srba, J.: A framework for relating timed transition systems and preserving TCTL model checking. In: Aldini, A., Bernardo, M., Bononi, L., Cortellessa, V. (eds.) EPEW 2010. LNCS, vol. 6342, pp. 83–98. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  34. 34.
    Jacobsen, L., Jacobsen, M., Møller, M.H., Srba, J.: A framework for relating timed transition systems and preserving TCTL model checking. Technical Report FIMU-RS-2010-09, Faculty of Informatics, Masaryk Univ. (2010c)Google Scholar
  35. 35.
    Janowska, A., Janowski, P., Wróblewski, D.: Translation of Intermediate Language to Timed Automata with Discrete Data. Fundamenta Informaticae 85(1-4), 235–248 (2008)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Lamport, L.: A fast mutual exclusion algorithm. ACM Transactions on Computer Systems 5(1), 1–11 (1987)CrossRefGoogle Scholar
  37. 37.
    Laroussinie, F., Larsen, K.G.: CMC: A tool for compositional model-checking of real-time systems. In: Proceedings of the FIP TC6 WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols (FORTE XI) and Protocol Specification, Testing and Verification (PSTV XVIII), pp. 439–456. Kluwer, B.V (1998)CrossRefGoogle Scholar
  38. 38.
    Mayr, E.W.: An algorithm for the general Petri net reachability problem (preliminary version). In: Proceedings of the 13th Ann. ACM Symposium on Theory of Computing, pp. 238–246. ACM, New York (1981)Google Scholar
  39. 39.
    Merlin, P.M.: A Study of the Recoverability of Computing Systems. PhD thesis, University of California, Irvine, CA, USA (1974)Google Scholar
  40. 40.
    Merlin, P.M., Faber, D.J.: Recoverability of communication protocols: Implications of a theoretical study. IEEE Transactions on Communications 24(9), 1036–1043 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)zbMATHGoogle Scholar
  42. 42.
    Nielsen, M., Sassone, V., Srba, J.: Properties of distributed timed-arc Petri nets. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2001. LNCS, vol. 2245, pp. 280–291. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  43. 43.
    Pelayo, F.L., Cuartero, F., Valero, V., Macia, H., Pelayo, M.L.: Applying timed-arc Petri nets to improve the performance of the MPEG-2 encoding algorithm. In: Proceedings of the 10th International Multimedia Modelling Conference (MMM 2004), pp. 49–56. IEEE Computer Society, Los Alamitos (2004)CrossRefGoogle Scholar
  44. 44.
    Pelayo, F.L., Cuartero, F., Valero, V., Pelayo, M.L., Merayo, M.G.: How does the memory work? by timed-arc Petri nets. In: Proceedings of the 4th IEEE International Conference on Cognitive Informatics (ICCI 2005), pp. 128–135 (2005)Google Scholar
  45. 45.
    Penczek, W., Pólrola, A.: Advances in Verification of Time Petri Nets and Timed Automata: A Temporal Logic Approach. Springer, Heidelberg (2006)CrossRefzbMATHGoogle Scholar
  46. 46.
    Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Darmstadt (1962)Google Scholar
  47. 47.
    Ramchandani, C.: Performance Evaluation of Asynchronous Concurrent Systems by Timed Petri Nets. PhD thesis, Massachusetts Institute of Technology, Cambridge (1973)Google Scholar
  48. 48.
    Ruiz, V.V., Cuartero Gomez, F., de Frutos Escrig, D.: On non-decidability of reachability for timed-arc Petri nets. In: Proceedings of the 8th International Workshop on Petri Net and Performance Models (PNPM 1999), pp. 188–196 (1999)Google Scholar
  49. 49.
    Ruiz, V.V., de Frutos Escrig, D., Marroquin Alonso, O.: Decidability of properties of timed-arc petri nets. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 187–206. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  50. 50.
    Ruiz, V.V., Pardo, J.J., Cuartero, F.: Translating TPAL specifications into timed-arc Petri nets. In: Esparza, J., Lakos, C.A. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 414–433. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  51. 51.
    Ruiz, V.V., Pelayo, F.L., Cuartero, F., Cazorla, D.: Specification and analysis of the MPEG-2 video encoder with timed-arc Petri nets. Electronic Notes Theoretial Computer Science 66(2) (2002)Google Scholar
  52. 52.
    Sifakis, J.: Use of Petri nets for performance evaluation. In: Proceedings of the Third International Symposium IFIP W.G. 7.3., Measuring, Modelling and Evaluating Computer Systems (Bonn-Bad Godesberg), pp. 75–93. Elsevier Science Publishers, Amsterdam (1977)Google Scholar
  53. 53.
    Sifakis, J., Yovine, S.: Compositional specification of timed systems. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 347–359. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  54. 54.
    Srba, J.: Timed-arc Petri nets vs. networks of timed automata. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 385–402. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  55. 55.
    Srba, J.: Comparing the expressiveness of timed automata and timed extensions of Petri nets. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 15–32. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  56. 56.
    Wang, J.: Timed Petri Nets, Theory and Application. Kluwer Academic Publishers, Dordrecht (1998) ISBN ISBN 0-7923-8270-6zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lasse Jacobsen
    • 1
  • Morten Jacobsen
    • 1
  • Mikael H. Møller
    • 1
  • Jiří Srba
    • 1
  1. 1.Department of Computer ScienceAalborg UniversityAalborg EastDenmark

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