Event Structure Semantics for Nominal Calculi

  • Roberto Bruni
  • Hernán Melgratti
  • Ugo Montanari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


Event structures have been used for giving true concurrent semantics to languages and models of concurrency such as CCS, Petri nets and graph grammars. Although certain nominal calculi have been modeled with graph grammars, and hence their event structure semantics could be obtained as instances of the general case, the main limitation is that in the case of graph grammars the construction is more complex than strictly necessary for dealing with usual nominal calculi and, speaking in categorical terms, it is not as elegant as in the case of Petri nets. The main contribution of this work is the definition of a particular class of graph grammars, called persistent, that are expressive enough to model name passing calculi while simplifying the denotational domain construction, which can be expressed as an adjunction. Finally, we apply our technique to derive event structure semantics for pi-calculus and join-calculus processes.


Event Structure Graph Transformation Graph Grammar Sequential Agent Typing Morphism 
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.


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  1. 1.
    Baldan, P.: Modelling concurrent computations: from contextual Petri nets to graph grammars. PhD thesis, University of Pisa (2000)Google Scholar
  2. 2.
    Baldan, P., Corradini, A., König, B.: Verifying Finite-State Graph Grammars: An Unfolding-Based Approach. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 83–98. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures and processes. Inform. and Comput. 171(1), 1–49 (2001)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Baldan, P., Corradini, A., Montanari, U., Ribeiro, L.: Concurrency and Nondeterminism in Graph Rewriting: From Graph Grammars to Asymmetric Event Structures and Backwards. Technical Report CS-2005-2, University Ca’ Foscari of Venice (2005)Google Scholar
  5. 5.
    Baldan, P., Gadducci, F., Montanari, U.: Concurrent Semantics for Graph Rewriting with Fusions. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Boreale, M., Sangiorgi, D.: A fully abstract semantics for causality in the pi-calculus. Acta Informatica 35(3), 353–400 (1998)CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Padberg, J.: The category of typed graph grammars and its adjunctions with categories of derivations. In: Proc. TAGT 1994. LNCS, vol. 1073, pp. 56–74. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: An event structure semantics for graph grammars with parallel productions. In: Proc. TAGT 1994. LNCS, vol. 1073, pp. 240–256. Springer, Heidelberg (1996)Google Scholar
  9. 9.
    Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fund. Inf. 26, 241–265 (1996)MathSciNetMATHGoogle Scholar
  10. 10.
    Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation I: Basic concepts and double pushout approach. In: [21]Google Scholar
  11. 11.
    Degano, P., Priami, C.: Non-interleaving semantics for mobile processes. Theoret. Comput. Sci. 216(1-2), 237–270 (1999)CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic approaches to graph transformation II: SPO approach and comparison with DPO. In: [21]Google Scholar
  13. 13.
    Fournet, C., Gonthier, G.: The reflexive chemical abstract machine and the Join calculus. In: Proc. POPL 1996, pp. 372–385. ACM Press, New York (1996)CrossRefGoogle Scholar
  14. 14.
    Gadducci, F.: Term Graph Rewriting for the phi-Calculus. In: Ohori, A. (ed.) APLAS 2003. LNCS, vol. 2895, pp. 37–54. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Gadducci, F., Montanari, U.: A Concurrent Graph Semantics for Mobile Ambients. In: Proc. MFPS 2001. ENTCS, vol. 45. Elsevier, Amsterdam (2001)Google Scholar
  16. 16.
    Golz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Information and Control 57, 125–147 (1983)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoret. Comput. Sci. 109, 181–224 (1993)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Meseguer, J., Montanari, U., Sassone, V.: On the semantics of Place/Transition Petri nets. Mathematical Structures in Computer Science 7, 359–397 (1997)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    Montanari, U., Pistore, M.: Concurent semantics for the π-calculus. ENTCS 1 (1995)Google Scholar
  20. 20.
    Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part 1. Theoret. Comput. Sci. 13, 85–108 (1981)CrossRefMathSciNetMATHGoogle Scholar
  21. 21.
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1. World Scientific, Singapore (1997)Google Scholar
  22. 22.
    Schied, G.: On relating Rewriting Systems and Graph Grammars to Event Structures. In: Ehrig, H., Schneider, H.-J. (eds.) Dagstuhl Seminar 1993. LNCS, vol. 776, pp. 326–340. Springer, Heidelberg (1994)Google Scholar
  23. 23.
    Varacca, D., Yoshida, N.: Typed event Structures and the π-calculus. In: Proc. MFPS 2006 (2006)Google Scholar
  24. 24.
    Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roberto Bruni
    • 1
  • Hernán Melgratti
    • 2
  • Ugo Montanari
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaItalia
  2. 2.IMT Lucca Institute for Advance StudiesItalia

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