A Polynomial Translation of π-Calculus (FCP) to Safe Petri Nets

  • Roland Meyer
  • Victor Khomenko
  • Reiner Hüchting
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7454)


We develop a polynomial translation from finite control processes (an important fragment of π-calculus) to safe low-level Petri nets. To our knowledge, this is the first such translation. It is natural (there is a close correspondence between the control flow of the original specification and the resulting Petri net), enjoys a bisimulation result, and it is suitable for practical model checking.


finite control process π-calculus Petri net model checking 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amadio, R., Meyssonnier, C.: On decidability of the control reachability problem in the asynchronous π-calculus. Nord. J. Comp. 9(1), 70–101 (2002)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Best, E., Devillers, R., Koutny, M.: Petri Net Algebra. Monographs in Theoretical Computer Science. An EATCS Series. Springer (2001)Google Scholar
  3. 3.
    Busi, N., Gorrieri, R.: Distributed semantics for the π-calculus based on Petri nets with inhibitor arcs. J. Log. Alg. Prog. 78(1), 138–162 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Dam, M.: Model checking mobile processes. Inf. Comp. 129(1), 35–51 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Devillers, R., Klaudel, H., Koutny, M.: A compositional Petri net translation of general π-calculus terms. For. Asp. Comp. 20(4-5), 429–450 (2008)zbMATHCrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Ferrari, G.-L., Gnesi, S., Montanari, U., Pistore, M.: A model-checking verification environment for mobile processes. ACM Trans. Softw. Eng. Methodol. 12(4), 440–473 (2003)CrossRefGoogle Scholar
  8. 8.
    Khomenko, V., Koutny, M., Niaouris, A.: Applying Petri net unfoldings for verification of mobile systems. In: Proc. of MOCA, Bericht FBI-HH-B-267/06, pp. 161–178. University of Hamburg (2006)Google Scholar
  9. 9.
    Khomenko, V., Meyer, R.: Checking π-calculus structural congruence is graph isomorphism complete. In: Proc. of ACSD, pp. 70–79. IEEE Computer Society Press (2009)Google Scholar
  10. 10.
    Meyer, R.: On Boundedness in Depth in the π-Calculus. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds.) IFIP TCS 2008. IFIP, vol. 273, pp. 477–489. Springer, Boston (2008)Google Scholar
  11. 11.
    Meyer, R.: A theory of structural stationarity in the π-calculus. Acta Inf. 46(2), 87–137 (2009)zbMATHCrossRefGoogle Scholar
  12. 12.
    Meyer, R., Gorrieri, R.: On the Relationship between π-Calculus and Finite Place/Transition Petri Nets. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 463–480. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Meyer, R., Khomenko, V., Hüchting, R.: A polynomial translation of π-calculus (FCP) to safe Petri nets. Technical Report CS-TR-1323, Newcastle Univ. (2012)Google Scholar
  14. 14.
    Meyer, R., Khomenko, V., Strazny, T.: A practical approach to verification of mobile systems using net unfoldings. Fundam. Inf. 94, 439–471 (2009)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Milner, R.: Communicating and Mobile Systems: the π-Calculus. CUP (1999)Google Scholar
  16. 16.
    Montanari, U., Pistore, M.: Checking Bisimilarity for Finitary π-Calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 42–56. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  17. 17.
    Orava, F., Parrow, J.: An algebraic verification of a mobile network. For. Asp. Comp. 4(6), 497–543 (1992)zbMATHCrossRefGoogle Scholar
  18. 18.
    Peschanski, F., Klaudel, H., Devillers, R.: A Petri Net Interpretation of Open Reconfigurable Systems. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 208–227. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Pistore, M.: History Dependent Automata. PhD thesis, Dipartimento di Informatica, Università di Pisa (1999)Google Scholar
  20. 20.
    Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. CUP (2001)Google Scholar
  21. 21.
    Victor, B., Moller, F.: The Mobility Workbench: A Tool for the π-Calculus. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 428–440. Springer, Heidelberg (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Roland Meyer
    • 1
  • Victor Khomenko
    • 2
  • Reiner Hüchting
    • 1
  1. 1.University of KaiserslauternGermany
  2. 2.Newcastle UniversityUK

Personalised recommendations