Efficient Contextual Unfolding

  • César Rodríguez
  • Stefan Schwoon
  • Paolo Baldan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)

Abstract

A contextual net is a Petri net extended with read arcs, which allow transitions to check for tokens without consuming them. Contextual nets allow for better modelling of concurrent read access than Petri nets, and their unfoldings can be exponentially more compact than those of a corresponding Petri net. A constructive but abstract procedure for generating those unfoldings was proposed in earlier work; however, no concrete implementation existed. Here, we close this gap providing two concrete methods for computing contextual unfoldings, with a view to efficiency. We report on experiments carried out on a number of benchmarks. These show that not only are contextual unfoldings more compact than Petri net unfoldings, but they can be computed with the same or better efficiency, in particular with respect to the place-replication encoding of contextual nets into Petri nets.

References

  1. 1.
    Baldan, P., Corradini, A., Montanari, U.: An event structure semantics for P/T contextual nets: Asymmetric event structures. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 63–80. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  2. 2.
    Baldan, P., Bruni, A., Corradini, A., König, B., Schwoon, S.: On the computation of mcMillan”s prefix for contextual nets and graph grammars. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 91–106. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Baldan, P., Corradini, A., König, B., Schwoon, S.: McMillan’s complete prefix for contextual nets. In: Jensen, K., van der Aalst, W.M.P., Billington, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency I. LNCS, vol. 5100, pp. 199–220. Springer, Heidelberg (2008)Google Scholar
  4. 4.
    Corbett, J.C.: Evaluating deadlock detection methods for concurrent software. IEEE Transactions on Software Engineering 22, 161–180 (1996)CrossRefGoogle Scholar
  5. 5.
    Esparza, J., Heljanko, K.: Implementing LTL model checking with net unfoldings. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, pp. 37–56. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Esparza, J., Heljanko, K.: Unfoldings - A Partial-Order Approach to Model Checking. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2008)Google Scholar
  7. 7.
    Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Formal Methods in System Design 20, 285–310 (2002)CrossRefMATHGoogle Scholar
  8. 8.
    Heljanko, K.: Deadlock and Reachability Checking with Finite Complete Prefixes. Licentiate’s thesis, Helsinki University of Technology (1999)Google Scholar
  9. 9.
    Janicki, R., Koutny, M.: Invariant semantics of nets with inhibitor arcs. In: Groote, J.F., Baeten, J.C.M. (eds.) CONCUR 1991. LNCS, vol. 527, pp. 317–331. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  10. 10.
  11. 11.
    McMillan, K.L.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–177. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  12. 12.
    Montanari, U., Rossi, F.: Contextual occurrence nets and concurrent constraint programming. In: Ehrig, H., Schneider, H.-J. (eds.) Dagstuhl Seminar 1993. LNCS, vol. 776. Springer, Heidelberg (1994)Google Scholar
  13. 13.
    Ristori, G.: Modelling Systems with Shared Resources via Petri Nets. Ph.D. thesis, Department of Computer Science, University of Pisa (1994)Google Scholar
  14. 14.
  15. 15.
    Rodríguez, C., Schwoon, S., Baldan, P.: Efficient contextual unfolding. Tech. Rep. LSV-11-14, LSV, ENS de Cachan (2011)Google Scholar
  16. 16.
  17. 17.
    Vogler, W., Semenov, A., Yakovlev, A.: Unfolding and finite prefix for nets with read arcs. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 501–516. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  18. 18.
    Winkowski, J.: Reachability in contextual nets. Fundamenta Informaticae 51(1-2), 235–250 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • César Rodríguez
    • 1
  • Stefan Schwoon
    • 1
  • Paolo Baldan
    • 2
  1. 1.LSV, ENS Cachan & CNRS, INRIA SaclayFrance
  2. 2.Dipartimento di Matematica Pura e ApplicataUniversità di PadovaItaly

Personalised recommendations