Representations of Petri Net Interactions

  • Paweł Sobociński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6269)


We introduce a novel compositional algebra of Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power.


Inference Rule Relational Form Operational Semantic Expressive Power Circuit Diagram 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramsky, S.: Abstract scalars, loops and free traced and strongly compact closed categories. In: Fiadeiro, J.L., Harman, N.A., Roggenbach, M., Rutten, J. (eds.) CALCO 2005. LNCS, vol. 3629, pp. 1–29. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Arbab, F.: Reo: a channel-based coordination model for component composition. Math. Struct. Comp. Sci. 14(3), 1–38 (2004)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Arbab, F., Bruni, R., Clarke, D., Lanese, I., Montanari, U.: Tiles for Reo. In: WADT 2008. LNCS, vol. 5486. Springer, Heidelberg (2008)Google Scholar
  4. 4.
    Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional modelling of reactive systems using open nets. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 502–518. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional semantics for open Petri nets based on deterministic processes. Math. Struct. Comp. Sci. 15(1), 1–35 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Baldan, P., Corradini, A., Ehrig, H., Heckel, R., König, B.: Bisimilarity and behaviour-preserving reconfigurations of Petri nets. Log. Meth. Comput. Sci. 4(4), 1–41 (2008)CrossRefGoogle Scholar
  7. 7.
    Best, E., Devillers, R., Hall, J.G.: The box calculus: A new causal algebra with multi-labelled communication. In: Rozenberg, G. (ed.) APN 1992. LNCS, vol. 609, pp. 21–69. Springer, Heidelberg (1992)Google Scholar
  8. 8.
    Bliudze, S., Sifakis, J.: A notion of glue expressiveness for component-based systems. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 508–522. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Bruni, R., Lanese, I., Montanari, U.: A basic algebra of stateless connectors. Theor. Comput. Sci. 366, 98–120 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Busi, N., Gorrieri, R.: A Petri net semantics for the π-calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 145–159. Springer, Heidelberg (1995)Google Scholar
  11. 11.
    Cerone, A.: Implementing Condition/Event nets in the circal process algebra. In: Kutsche, R.-D., Weber, H. (eds.) FASE 2002. LNCS, vol. 2306, pp. 49–63. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Degano, P., Nicola, R.D., Montanari, U.: A distributed operational semantics for CCS based on C/E systems. Acta Inform. 26, 59–91 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Gadducci, F., Montanari, U.: The tile model. In: Proof, Language and Interaction: Essays in Honour of Robin Milner, pp. 133–166. MIT Press, Cambridge (2000)Google Scholar
  14. 14.
    Goltz, U.: CCS and Petri nets. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469. Springer, Heidelberg (1990)Google Scholar
  15. 15.
    Groote, J.F., Voorhoeve, M.: Operational semantics for Petri net components. Theor. Comput. Sci. 379(1-2), 1–19 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Joyal, A., Street, R.: The geometry of tensor calculus, i. Adv. Math. 88, 55–112 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Katis, P., Sabadini, N., Walters, R.F.C.: Representing P/T nets in Span(Graph). In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 307–321. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  18. 18.
    Katis, P., Sabadini, N., Walters, R.F.C.: Span(Graph): an algebra of transition systems. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 322–336. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  19. 19.
    Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Automata Studies, pp. 3–41. Princeton University Press, Princeton (1956)Google Scholar
  20. 20.
    Koutny, M., Esparza, J., Best, E.: Operational semantics for the Petri box calculus. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 210–225. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  21. 21.
    Leifer, J.J., Milner, R.: Transition systems, link graphs and Petri nets. Math. Struct. Comp. Sci. 16(6), 989–1047 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    McNaughton, R., Yamada, H.: Regular expressions and state graphs for automata. IEEE Trans. Electronic Computers 9, 39–47 (1960)CrossRefGoogle Scholar
  23. 23.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)Google Scholar
  24. 24.
    Milner, R.: Bigraphs for Petri nets. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. LNCS, vol. 3098, pp. 686–701. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  25. 25.
    Montanari, U., Rossi, F.: Contextual nets. Acta Inform. 32(6), 545–596 (1995)zbMATHMathSciNetGoogle Scholar
  26. 26.
    Nielsen, M., Priese, L., Sassone, V.: Characterizing behavioural congruences for Petri nets. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 175–189. Springer, Heidelberg (1995)Google Scholar
  27. 27.
    Plotkin, G.D.: A structural approach to operational semantics. J. Logic Algebr. Progr. 60-61, 17–139 (2004); Originally appeared as Technical Report DAIMI FN-19, University of Aarhus (1981)CrossRefMathSciNetGoogle Scholar
  28. 28.
    Reisig, W.: Petri nets: an introduction. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1985)zbMATHGoogle Scholar
  29. 29.
    Sassone, V., Sobociński, P.: A congruence for Petri nets. In: Petri Nets and Graph Transformation (PNGT 2004). ENTCS, vol. 127, pp. 107–120 (2005)Google Scholar
  30. 30.
    Sobociński, P.: A non-interleaving process calculus for multi-party synchronisation. In: Interaction and Concurrency (ICE 2009). EPTCS, vol. 12 (2009)Google Scholar
  31. 31.
    van Glabbeek, R., Vaandrager, F.: Petri net models for algebraic theories of concurrency. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259. Springer, Heidelberg (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Paweł Sobociński
    • 1
  1. 1.ECSUniversity of SouthamptonUK

Personalised recommendations