Encoding Asynchronous Interactions Using Open Petri Nets

  • Paolo Baldan
  • Filippo Bonchi
  • Fabio Gadducci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5710)


We present an encoding for (bound) processes of the asynchronous CCS with replication into open Petri nets: ordinary Petri nets equipped with a distinguished set of open places. The standard token game of nets models the reduction semantics of the calculus; the exchange of tokens on open places models the interactions between processes and their environment. The encoding preserves strong and weak CCS asynchronous bisimilarities: it thus represents a relevant step in establishing a precise correspondence between asynchronous calculi and (open) Petri nets. The work is intended as fostering the technology transfer between these formalisms: as an example, we discuss how some results on expressiveness can be transferred from the calculus to nets and back.


Asynchronous calculi bisimilarity decidability open Petri nets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Honda, K., Tokoro, M.: An object calculus for asynchronous communication. In: America, P. (ed.) ECOOP 1991. LNCS, vol. 512, pp. 133–147. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  2. 2.
    Boudol, G.: Asynchrony and the π-calculus. Technical Report 1702, INRIA, Sophia Antipolis (1992)Google Scholar
  3. 3.
    De Nicola, R., Ferrari, G., Pugliese, R.: KLAIM: A kernel language for agents interaction and mobility. IEEE Trans. Software Eng. 24(5), 315–330 (1998)CrossRefGoogle Scholar
  4. 4.
    Castellani, I., Hennessy, M.: Testing theories for asynchronous languages. In: Arvind, V., Sarukkai, S. (eds.) FST TCS 1998. LNCS, vol. 1530, pp. 90–102. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Ferrari, G., Guanciale, R., Strollo, D.: Event based service coordination over dynamic and heterogeneous networks. In: Dan, A., Lamersdorf, W. (eds.) ICSOC 2006. LNCS, vol. 4294, pp. 453–458. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Amadio, R., Castellani, I., Sangiorgi, D.: On bisimulations for the asynchronous pi-calculus. TCS 195(2), 291–324 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Boreale, M., De Nicola, R., Pugliese, R.: Asynchronous observations of processes. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 95–109. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Boreale, M., De Nicola, R., Pugliese, R.: A theory of “may” testing for asynchronous languages. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 165–179. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Rathke, J., Sobocinski, P.: Making the unobservable, unobservable. In: ICE 2008. ENTCS. Elsevier, Amsterdam (2009) (to appear) Google Scholar
  10. 10.
    Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1985)CrossRefzbMATHGoogle Scholar
  11. 11.
    van der Aalst, W.: Pi calculus versus Petri nets: Let us eat “humble pie” rather than further inflate the “Pi hype”. BPTrends 3(5), 1–11 (2005)Google Scholar
  12. 12.
    Goltz, U.: CCS and Petri nets. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 334–357. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  13. 13.
    Gorrieri, R., Montanari, U.: SCONE: A simple calculus of nets. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 2–31. Springer, Heidelberg (1990)Google Scholar
  14. 14.
    Busi, N., Gorrieri, R.: A Petri net semantics for pi-calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 145–159. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  15. 15.
    Devillers, R., Klaudel, H., Koutny, M.: A compositional Petri net translation of general pi-calculus terms. Formal Asp. Comput. 20(4-5), 429–450 (2008)CrossRefzbMATHGoogle Scholar
  16. 16.
    Aranda, J., Valencia, F., Versari, C.: On the expressive power of restriction and priorities in CCS with replication. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 242–256. Springer, Heidelberg (2009)Google Scholar
  17. 17.
    Olderog, E.: Nets, terms and formulas. Cambridge University Press, Cambridge (1991)CrossRefzbMATHGoogle Scholar
  18. 18.
    Busi, N., Gorrieri, R.: Distributed semantics for the π-calculus based on Petri nets with inhibitor arcs. Journal of Logic and Algebraic Programming 78, 138–162 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Berry, G., Boudol, G.: The chemical abstract machine. TCS 96, 217–248 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Milner, R., Sangiorgi, D.: Barbed bisimulation. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 685–695. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  21. 21.
    Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional semantics for open Petri nets based on deterministic processes. Mathematical Structures in Computer Science 15(1), 1–35 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    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
  23. 23.
    Sassone, V., Sobociński, P.: A congruence for Petri nets. In: Ehrig, H., Padberg, J., Rozenberg, G. (eds.) PNGT 2004. ENTCS, vol. 127, pp. 107–120. Elsevier, Amsterdam (2005)Google Scholar
  24. 24.
    Vogler, W.: Modular Construction and Partial Order Semantics of Petri Nets. LNCS, vol. 625. Springer, Heidelberg (1992)zbMATHGoogle Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    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
  27. 27.
    Kindler, E.: A compositional partial order semantics for Petri net components. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 235–252. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  28. 28.
    Busi, N., Gabbrielli, M., Zavattaro, G.: Comparing recursion, replication, and iteration in process calculi. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 307–319. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  29. 29.
    Jancar, P.: Undecidability of bisimilarity for Petri nets and some related problems. TCS 148(2), 281–301 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Buscemi, M., Sassone, V.: High-level Petri nets as type theories in the join calculus. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 104–120. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  31. 31.
    Busi, N., Zavattaro, G.: A process algebraic view of shared dataspace coordination. J. Log. Algebr. Program. 75(1), 52–85 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Devillers, R., Klaudel, H., Koutny, M.: A Petri net semantics of a simple process algebra for mobility. In: Baeten, J., Phillips, I. (eds.) EXPRESS 2005. ENTCS, vol. 154, pp. 71–94. Elsevier, Amsterdam (2006)Google Scholar
  33. 33.
    Meyer, R., Khomenko, V., Strazny, T.: A practical approach to verification of mobile systems using net unfoldings. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 327–347. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  34. 34.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)CrossRefzbMATHGoogle Scholar
  35. 35.
    Sangiorgi, D.: On the bisimulation proof method. Mathematical Structures in Computer Science 8(5), 447–479 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Gadducci, F.: Graph rewriting and the π-calculus. Mathematical Structures in Computer Science 17, 1–31 (2007)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Milner, R.: Pure bigraphs: Structure and dynamics. Information and Computation 204, 60–122 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Esparza, J., Nielsen, M.: Decidability issues for Petri nets - a survey. Journal Inform. Process. Cybernet. EIK 30(3), 143–160 (1994)zbMATHGoogle Scholar
  39. 39.
    Agerwala, T., Flynn, M.: Comments on capabilities, limitations and “correctness” of Petri nets. Computer Architecture News 4(2), 81–86 (1973)CrossRefGoogle Scholar
  40. 40.
    Busi, N., Zavattaro, G.: Expired data collection in shared dataspaces. TCS 3(298), 529–556 (2003)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paolo Baldan
    • 1
  • Filippo Bonchi
    • 2
    • 3
  • Fabio Gadducci
    • 3
  1. 1.Dipartimento di Matematica Pura e ApplicataUniversità di PadovaItaly
  2. 2.Centrum voor Wiskunde en Informatica, AmsterdamNetherlands
  3. 3.Dipartimento di InformaticaUniversità di PisaItaly

Personalised recommendations