Skip to main content
SpringerLink
Log in

Using transition set sequences to partition behaviors of petri nets

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

The transition set semantics (Wang and Jiao, LNCS 6128:84–103, 2010) partitions the Petri net behaviors in a canonical way such that behaviors in an equivalence class have the same canonical transition set sequence. This article extends the semantics in two ways: firstly, the semantics is parameterized by the basic relation on the structural transitions to define different variants; secondly, the semantics for the infinite firing sequences of the net is defined. We prove that these extensions still preserve the well-definedness, soundness and completeness of the semantics. Furthermore, we show how to recognize some infinite sequences called back-loops in the view of this new semantics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems, LNCS 1579, pp. 193–207. Springer (1999)

  2. Best E., Devillers R.: Sequential and concurrent behaviour in Petri net theory. Theor. Comput. Sci. 55(1), 87–136 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Best E., Darondeau P.: A decomposition theorem for finite persistent transition systems. Acta Informatica 46, 237–254 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bonizzoni, P., Mauri, G., Pighizzini, G.: About infinite traces. In: Proceedings of the ASMICS Workshop on Partially Commutative Monoids, Tech. Rep. TUM-I 9002, Technische Universität München (1989)

  5. Burkhard, H.-D.: The Maximum Firing Strategy in Petri nets gives more power. ICS-PAS Report no. 411: pp. 24–26, Warschau (1980)

  6. Cartier P., Foata D.: Problèmes combinatoires de commutation et rédarrangements LNCS 85. Springer, Berlin, Heidelberg, New York (1969)

    Google Scholar 

  7. Diekert V.: A partial trace semantics for Petri nets. Theor. Comput. Sci. 134(1), 87–105 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Diekert V., Metivier Y.: Partial commutation and traces. In: Rozenberg, G., Salomaa, A. (eds) Handbook of formal languages vol 3., pp. 457–534. Springer, Berlin (1997)

    Chapter  Google Scholar 

  9. Heljanko, K.: Bounded reachability checking with process semantics. In: Proceedings of 12th International Conference on Concurrency Theory, LNCS 2154, pp. 218–232, Springer (2001)

  10. Janicki R., Koutny M.: Semantics of inhibitor nets. Inf. Comput. 123, 1–16 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Petri Nets: Applications and Relationships to Other Models of Concurrency, LNCS 255, pp. 279–324. Springer (1987)

  12. Ochmanski E.: Semi-commutations for place/transition systems. Bull. Eur. Assoc. Theor. Comput. Sci. (EATCS) 38, 166–191 (1989)

    Google Scholar 

  13. Rozenberg G., Engelfriet J.: Elementary net systems. In: Reisig, W., Rozenberg, G. (eds) Lectures on Petri Nets I Basic Models Advances in Petri Nets LNCS 1491., pp. 12–121. Springer, Berlin (1998)

    Google Scholar 

  14. Reisig W.: Petri nets: An introduction. Springer, Berlin, Heidelberg, New York, Tokyo (1985)

    MATH  Google Scholar 

  15. Thanh H.C.: Transforming sequential processes of net systems into concurrent ones. KES J. 11(6), 391–397 (2007)

    Google Scholar 

  16. Wang, Y., Jiao, L.: Canonical Transition Set Semantics for Petri Nets. In: Proceedings of 31st International Conference on Application and Theory of Petri Nets and Other Models of Concurrency, LNCS 6128, pp. 84–103, Springer (2010)

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, 4# South Fourth Street, Zhong Guan Cun, Beijing, People’s Republic of China

    Yunhe Wang & Li Jiao

  2. Graduate University of Chinese Academy of Sciences, Beijing, People’s Republic of China

    Yunhe Wang

Authors
  1. Yunhe Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Jiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunhe Wang.

Additional information

This research was financially supported by the National Natural Science Foundation of China (Grant No. 60970029).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Y., Jiao, L. Using transition set sequences to partition behaviors of petri nets. Acta Informatica 49, 15–28 (2012). https://doi.org/10.1007/s00236-011-0147-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-011-0147-6

Keywords

Search

Navigation