Flow Unfolding of Multi-clock Nets

  • Giovanni Casu
  • G. Michele Pinna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8489)


Unfoldings of nets are often related to event structures: each execution of a net can be viewed as a configuration in the associated event structure. This allows for a clear characterization of dependencies and the conflicts between occurrences of transitions in the net. This relation is somehow lost if more compact representations of the executions of nets are considered, e.g. in trellises or merged processes of multi-clock nets. In this paper we introduce an unfolding, called flow unfolding, that turns out to be related to flow event structures, hence dependencies and conflict are still represented. Furthermore, this unfolding gives also a more compact representation of the executions of a multi-clock net, similarly to what approaches like trellises or merged processes do.


Event Structure Labelling Function Causal Dependency Control Place Merge Process 
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.
    Khomenko, V.: Model Checking based on Prefixes of Petri Net Unfoldings. PhD thesis, School of Computing Science, University of Newcastle upon Tyne (2003)Google Scholar
  2. 2.
    Fabre, E., Benveniste, A., Haar, S., Jard, C.: Distributed Monitoring of Concurrent and Asynchronous Systems. Discrete Event Dynamic Systems 15, 33–84 (2005)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)Google Scholar
  4. 4.
    Engelfriet, J.: Branching processes of Petri nets. Acta Informatica 28, 575–591 (1991)MathSciNetCrossRefGoogle Scholar
  5. 5.
    McMillan, K.: A Technique of State Space Search Based on Unfolding. Formal Methods in System Design 6, 45–65 (1995)CrossRefGoogle Scholar
  6. 6.
    Fabre, E.: Trellis processes: A compact representation for runs of concurrent systems. Discrete Event Dynamic Systems 17, 267–306 (2007)CrossRefGoogle Scholar
  7. 7.
    Khomenko, V., Kondratyev, A., Koutny, M., Vogler, W.: Merged Processes: a new condensed representation of Petri net behaviour. Acta Informatica 43, 307–330 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    van Glabbeek, R.J., Plotkin, G.D.: Configuration structures, event structures and Petri nets. Theoretical Computer Science 410, 4111–4159 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pinna, G.M., Poigné, A.: On the nature of events: another perspective in concurrency. Theoretical Computer Science 138, 425–454 (1995)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Boudol, G.: Flow Event Structures and Flow Nets. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 62–95. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  11. 11.
    Boudol, G., Castellani, I.: Flow models of distributed computations: Three equivalent semantics for CCS. Information and Computation 114, 247–314 (1994)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures and processes. Information and Computation 171, 1–49 (2001)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Baldan, P., Busi, N., Corradini, A., Pinna, G.M.: Domain and event structure semantics for Petri nets with read and inhibitor arcs. Theoretical Computer Science 323, 129–189 (2004)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Langerak, R.: Bundle Event Structures: A Non-Interleaving Semantics for Lotos. In: Diaz, M., Groz, R. (eds.) Fifth International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols, FORTE 1992, IFIP Transactions C-10, pp. 331–346. North-Holland (1992)Google Scholar
  15. 15.
    Gunawardena, J.: A generalized event structure for the Muller unfolding of a safe net. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 278–292. Springer, Heidelberg (1993)Google Scholar
  16. 16.
    Pinna, G.M.: How much is worth to remember? A taxonomy based on Petri Nets Unfoldings. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 109–128. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    van Glabbeek, R.J., Plotkin, G.D.: Configuration structures. In: Kozen, D. (ed.) Proceedings of 10th Annual IEEE Symposium on Logic in Computer Science, pp. 199–209. IEEE Computer Society Press (1995)Google Scholar
  18. 18.
    Reisig, W.: Petri Nets: An Introduction. EACTS Monographs on Theoretical Computer Science. Springer (1985)Google Scholar
  19. 19.
    Hayman, J., Winskel, G.: The unfolding of general Petri nets. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), Dagstuhl, Germany, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2008)Google Scholar
  20. 20.
    Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85–108 (1981)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Esparza, J., Römer, S., Vogler, W.: An Improvement of McMillan’s Unfolding Algorithm. Formal Methods in System Design 20, 285–310 (2002)CrossRefGoogle Scholar
  22. 22.
    Khomenko, V., Mokhov, A.: Direct construction of Complete Merged Processes. The Computer Journal (2013) (to appear)Google Scholar
  23. 23.
    Rathke, J., Sobocinski, P., Stephens, O.: Decomposing Petri nets. CoRR abs/1304.3121 (2013)Google Scholar
  24. 24.
    Khomenko, V., Koutny, M., Vogler, W.: Canonical prefixes of Petri net unfoldings. Acta Informatica 40, 95–118 (2003)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Balaguer, S., Chatain, T., Haar, S.: Building occurrence nets from reveals relations. Fundamamenta Informaticae 123, 245–272 (2013)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Haar, S., Kern, C., Schwoon, S.: Computing the reveals relation in occurrence nets. Theoretical Computer Science 493, 66–79 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Giovanni Casu
    • 1
  • G. Michele Pinna
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly

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