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Verification of Timed-Arc Petri Nets

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SOFSEM 2011: Theory and Practice of Computer Science (SOFSEM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6543))

Abstract

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.

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References

  1. TAPAAL, http://www.tapaal.net

  2. UPPAAL, http://www.uppaal.com

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. Boucheneb, H., Gardey, G., Roux, O.H.: TCTL model checking of time Petri nets. Journal of Logic and Computation 19(6), 1509–1540 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  26. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256(1-2), 63–92 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  28. Hack, M.: Petri Net Language. Technical Report MIT-LCS-TR-159, Massachusetts Institute of Technology, Cambridge, MA, USA (1976)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  30. Heitmann, F., Moldt, D., Mortensen, K.H., Rölke, H.: Petri nets tools database quick overview, http://www.informatik.uni-hamburg.de/TGI/PetriNets/tools/quick.html (accessed: 28.10.2010)

  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 978-3-939897-15-6

    Google Scholar 

  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.net

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Janowska, A., Janowski, P., Wróblewski, D.: Translation of Intermediate Language to Timed Automata with Discrete Data. Fundamenta Informaticae 85(1-4), 235–248 (2008)

    MathSciNet  MATH  Google Scholar 

  36. Lamport, L.: A fast mutual exclusion algorithm. ACM Transactions on Computer Systems 5(1), 1–11 (1987)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Merlin, P.M.: A Study of the Recoverability of Computing Systems. PhD thesis, University of California, Irvine, CA, USA (1974)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  41. Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Penczek, W., Pólrola, A.: Advances in Verification of Time Petri Nets and Timed Automata: A Temporal Logic Approach. Springer, Heidelberg (2006)

    Book  MATH  Google Scholar 

  46. Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Darmstadt (1962)

    Google Scholar 

  47. Ramchandani, C.: Performance Evaluation of Asynchronous Concurrent Systems by Timed Petri Nets. PhD thesis, Massachusetts Institute of Technology, Cambridge (1973)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  56. Wang, J.: Timed Petri Nets, Theory and Application. Kluwer Academic Publishers, Dordrecht (1998) ISBN ISBN 0-7923-8270-6

    MATH  Google Scholar 

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Jacobsen, L., Jacobsen, M., Møller, M.H., Srba, J. (2011). Verification of Timed-Arc Petri Nets. In: Černá, I., et al. SOFSEM 2011: Theory and Practice of Computer Science. SOFSEM 2011. Lecture Notes in Computer Science, vol 6543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18381-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-18381-2_4

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