Petri Net Semantics of the Finite π-Calculus

  • Raymond Devillers
  • Hanna Klaudel
  • Maciej Koutny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3235)


In this paper we propose a translation into high level Petri nets of a finite fragment of the π-calculus. Our construction renders in a compositional way the control flow aspects present in π-calculus process expressions, by adapting the existing graph-theoretic net composition operators. Those aspects which are related to term rewriting, as well as name binding, are handled through special inscription of places, transitions and arcs, together with a suitable choice of the initial marking for a compositionally derived high level Petri net.


  1. 1.
    Best, E., Devillers, R.: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science 55, 87–136 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Best, E., Frączak, W., Hopkins, R.P., Klaudel, H., Pelz, E.: M-nets: an Algebra of High Level Petri Nets, with an Application to the Semantics of Concurrent Programming Languages. Acta Informatica 35, 813–857 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Best, E., Devillers, R., Koutny, M.: Petri Net Algebra. EATCS Monographs on TCS. Springer, Heidelberg (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Boreale, M., Sangiorgi, D.: A Fully Abstract Semantics for Causality in the π- calculus. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 243–254. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  5. 5.
    Busi, N., Gorrieri, R.: A Petri net Semantics for π-calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 145–159. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  6. 6.
    Cattani, G.L., Sewell, P.: Models for Name-Passing Processes: Interleaving and Causal. In: Proc. of LICS 2000, pp. 322–333. IEEE CS Press, Los Alamitos (2000)Google Scholar
  7. 7.
    Cattani, G.L., Sewell, P.: Models for Name-Passing Processes: Interleaving and Causal. Technical Report TR-505, University of Cambridge (2000)Google Scholar
  8. 8.
    Christensen, S., Hansen, N.D.: Coloured Petri Nets Extended with Place Capacities, Test Arcs and Inhibitor Arcs. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 186–205. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  9. 9.
    Devillers, R., Klaudel, H., Koutny, M.: Petri net semantics of the finite π-calculus CS-TR-846 University of Newcastle (2004)Google Scholar
  10. 10.
    Engelfriet, J.: A Multiset Semantics for the π-calculus with Replication. Theoretical Computer Science 153, 65–94 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Klaudel, H., Pommereau, F.: Asynchronous links in the PBC and M-nets. In: Thiagarajan, P.S., Yap, R.H.C. (eds.) ASIAN 1999. LNCS, vol. 1742, pp. 190–200. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  13. 13.
    Milner, R., Parrow, J., Walker, D.: A Calculus of Mobile Processes. Information and Computation 100, 1–77 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Montanari, U., Pistore, M.: Concurrent Semantics for the π-calculus. In: Proc. of MFPS 1995. Electronic Notes in Computer Science, vol. 1, Elsevier, Amsterdam (1995)Google Scholar
  15. 15.
    Parrow, J.: An Introduction to the π-calculus. In: Bergstra, Ponse, Smolka (eds.) Handbook of Process Algebra, pp. 479–543. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  16. 16.
    Plotkin, G.D.: A Structural Approach to Operational Semantics. Technical Report FN-19, Computer Science Department, University of Aarhus (1981)Google Scholar
  17. 17.
    Vogler, W.: Partial Order Semantics and Read Arcs. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 508–517. Springer, Heidelberg (1997)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2004

Authors and Affiliations

  • Raymond Devillers
    • 1
  • Hanna Klaudel
    • 2
  • Maciej Koutny
    • 3
  1. 1.Université Libre de BruxellesBruxellesBelgium
  2. 2.Université d’Évry, LaMIÉvryFrance
  3. 3.University of NewcastleU.K.

Personalised recommendations