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On the Relationship between π-Calculus and Finite Place/Transition Petri Nets

  • Conference paper
CONCUR 2009 - Concurrency Theory (CONCUR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5710))

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Abstract

We clarify the relationship between π-calculus and finite p/t Petri nets. The first insight is that the concurrency view to processes taken in [Eng96, AM02, BG09] and the structural view in [Mey09] are orthogonal. This allows us to define a new concurrency p/t net semantics that can be combined with the structural semantics in [Mey09]. The result is a more expressive mixed semantics, which translates precisely the so-called mixed-bounded processes into finite p/t nets. Technically, the translation relies on typing of restricted names. As second main result we show that mixed-bounded processes form the borderline to finite p/t nets. For processes just beyond this class reachability becomes undecidable and so no faithful translation into finite p/t nets exists.

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References

  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)

    MathSciNet  MATH  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  4. Busi, N., Gabbrielli, M., Zavattaro, G.: Replication vs. recursive definitions in channel based calculi. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 133–144. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. Dam, M.: Model checking mobile processes. Inf. Comp. 129(1), 35–51 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. 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)

    Article  MATH  Google Scholar 

  9. Engelfriet, J., Gelsema, T.: Multisets and structural congruence of the pi-calculus with replication. Theor. Comp. Sci. 211(1-2), 311–337 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Engelfriet, J., Gelsema, T.: A new natural structural congruence in the pi-calculus with replication. Acta Inf. 40(6), 385–430 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Engelfriet, J.: A multiset semantics for the pi-calculus with replication. Theor. Comp. Sci. 153(1-2), 65–94 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. Fokkink, W.: Modelling Distributed Systems. Springer, Heidelberg (2007)

    Google Scholar 

  14. 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 

  15. Mayr, E.W.: An algorithm for the general Petri net reachability problem. SIAM J. Comp. 13(3), 441–460 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  16. Meyer, R.: On boundedness in depth in the π-calculus. In: Proc. of IFIP TCS. IFIP, vol. 273, pp. 477–489. Springer, Heidelberg (2008)

    Google Scholar 

  17. Meyer, R.: Structural Stationarity in the π-calculus. PhD thesis, Department of Computing Science, University of Oldenburg (2008)

    Google Scholar 

  18. Meyer, R.: A theory of structural stationarity in the π-calculus. Acta Inf. 46(2), 87–137 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Milner, R.: Communication and concurrency. Prentice Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  20. Milner, R.: Communicating and Mobile Systems: the π-Calculus. CUP, Cambridge (1999)

    MATH  Google Scholar 

  21. Minsky, M.: Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  22. Meyer, R., Khomenko, V., Strazny, T.: A practical approach to verification of mobile systems using net unfoldings. Fund. Inf. (to appear 2009)

    Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Petruchio (2008), http://petruchio.informatik.uni-oldenburg.de

  25. Pistore, M.: History Dependent Automata. PhD thesis, Dipartimento di Informatica, Università di Pisa (1999)

    Google Scholar 

  26. Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. CUP, Cambridge (2001)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LIAFA, Paris Diderot University & CNRS, France

    Roland Meyer

  2. Department of Computing Science, University of Bologna, Italy

    Roberto Gorrieri

Authors
  1. Roland Meyer
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  2. Roberto Gorrieri
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Bologna, Mura A. Zamboni 7, 40127, Bologna, Italy

    Mario Bravetti  & Gianluigi Zavattaro  & 

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Meyer, R., Gorrieri, R. (2009). On the Relationship between π-Calculus and Finite Place/Transition Petri Nets. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_31

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  • DOI: https://doi.org/10.1007/978-3-642-04081-8_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04080-1

  • Online ISBN: 978-3-642-04081-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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