On the Step Branching Time Closure of Free-Choice Petri Nets

  • Stephan Mennicke
  • Jens-Wolfhard Schicke-Uffmann
  • Ursula Goltz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8461)


Free-choice Petri nets constitute a non-trivial subclass of Petri nets, excelling in simplicity as well as in analyzability. Extensions of free-choice nets have been investigated and shown to be translatable back to interleaving-equivalent free-choice nets. In this paper, we investigate extensions of free-choice Petri nets up to step branching time equivalences. For extended free-choice nets, we achieve a generalization of the equivalence result by showing that an existing construction respects weak step bisimulation equivalence. The known translation for behavioral free-choice does not respect step branching time equivalences, which turns out to be a property inherent to all transformation functions from this net class into (extended) free-choice Petri nets. By analyzing the critical structures, we find two subsets of behavioral free-choice nets that are step branching time equivalent to free-choice nets. Finally, we provide a discussion concerning the actual closure of free-choice Petri nets up to step branching time equivalences.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Best, E.: Structure theory of petri nets: the free choice hiatus. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 168–205. Springer, Heidelberg (1987)Google Scholar
  2. 2.
    Best, E., Shields, M.W.: Some equivalence results for free choice nets and simple nets and on the periodicity of live free choice nets. In: Protasi, M., Ausiello, G. (eds.) CAAP 1983. LNCS, vol. 159, pp. 141–154. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  3. 3.
    Best, E., Wimmel, H.: Structure theory of petri nets. In: Jensen, K., van der Aalst, W.M.P., Balbo, G., Koutny, M., Wolf, K. (eds.) Transactions on Petri Nets and Other Models of Concurrency VII. LNCS, vol. 7480, pp. 162–224. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge University Press, New York (1995)CrossRefMATHGoogle Scholar
  5. 5.
    Esparza, J.: Decidability and complexity of petri net problems – an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    van Glabbeek, R.J.: The linear time - branching time spectrum. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 278–297. Springer, Heidelberg (1990)Google Scholar
  7. 7.
    van Glabbeek, R.J., Goltz, U., Schicke, J.-W.: On synchronous and asynchronous interaction in distributed systems. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 16–35. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    van Glabbeek, R.J., Goltz, U., Schicke, J.W.: Symmetric and asymmetric asynchronous interaction. In: ICE 2008, Satellite Workshop ICALP 2008. ENTCS, vol. 229, pp. 77–95. Elsevier (2009)Google Scholar
  9. 9.
    van Glabbeek, R.J., Goltz, U., Schicke, J.W.: Abstract processes of place/transition systems. Information Processing Letters 111(13), 626–633 (2011)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    van Glabbeek, R.J., Goltz, U., Schicke-Uffmann, J.W.: On characterising distributability. LMCS 9(3) (2013)Google Scholar
  11. 11.
    Mennicke, S.: Strong Distributability Criteria for Petri Nets. Master’s thesis, TU Braunschweig, Germany (May 2013)Google Scholar
  12. 12.
    Petri, C.A.: Kommunikation mit Automaten. Ph.D. thesis, TU Darmstadt (1962)Google Scholar
  13. 13.
    Rozenberg, G., Thiagarajan, P.: Petri nets: Basic notions, structure, behaviour. In: Rozenberg, G., de Bakker, J.W., de Roever, W.-P. (eds.) Current Trends in Concurrency. LNCS, vol. 224, pp. 585–668. Springer, Heidelberg (1986)CrossRefGoogle Scholar
  14. 14.
    Vidal-Naquet, G.: Deterministic languages of petri nets. In: Girault, C., Reisig, W. (eds.) Application and Theory of Petri Nets. Informatik-Fachberichte, vol. 52, pp. 198–202. Springer, Heidelberg (1982)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Stephan Mennicke
    • 1
  • Jens-Wolfhard Schicke-Uffmann
    • 1
  • Ursula Goltz
    • 1
  1. 1.TU BraunschweigGermany

Personalised recommendations