Simultaneity in Event Structures

  • G. Michele Pinna
  • Andrea Saba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6108)


Various brand of event structures, prime, bundle, flow, asymmetric, inhibitor just to mention some, have been proposed to face the various kinds of causality and conflict arising in computation. The notion of simultaneity, i.e., the faithful representation that certain events have to occur together, is usually left out from the models for concurrent computations, with some notably exceptions like Pratt’s Chu spaces or Bruni&Montanari’s Zero-Safe nets. In this paper we propose a notion of event structures with simultaneity to take into account the simultaneity and we relate the introduced notion with the prime event structures and domains.


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  1. 1.
    Abbes, S.: A cartesian closed category of event structures with quotients. Discrete Mathematics & Theor. Comput. Sci. 8(1), 249–272 (2006)MATHMathSciNetGoogle Scholar
  2. 2.
    Baldan, P., Busi, N., Corradini, A., Pinna, G.M.: Domain and event structure semantics for Petri nets with read and inhibitor arcs. Theor. Comput. Sci. 323(1-3), 129–189 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures and processes. Inf. Comput. 171(1), 1–49 (2001)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Boudol, G.: Flow Event Structures and Flow Nets. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 62–95. Springer, Heidelberg (1990)Google Scholar
  5. 5.
    Bruni, R., Montanari, U.: Zero-safe nets: Comparing the collective and individual token approaches. Inf. Comput. 156(1-2), 46–89 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Busi, N.: Causality in membrane systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 160–171. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Goltz, U., Reisig, W.: The non-sequential behavior of Petri nets. Information and Control 57(2/3), 125–147 (1983)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gunawardena, J.: Geometric logic, causality and event structures. In: Groote, J.F., Baeten, J.C.M. (eds.) CONCUR 1991. LNCS, vol. 527, pp. 266–280. Springer, Heidelberg (1991)Google Scholar
  9. 9.
    Gunawardena, J.: Causal automata. Theor. Comput. Sci. 101(2), 265–288 (1992)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hoogers, P.W., Kleijn, H.C.M., Thiagarajan, P.S.: An event structure semantics for general Petri nets. Theor. Comput. Sci. 153(1-2), 129–170 (1996)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Janicki, R., Koutny, M.: Semantics of inhibitor nets. Inf. Comput. 123, 1–16 (1995)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Janicki, R.: Relational structures model of concurrency. Acta Inf. 45(4), 279–320 (2008)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Janicki, R., Koutny, M.: Structure of concurrency. Theor. Comput. Sci. 112(1), 5–52 (1993)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Juhás, G., Lorenz, R., Mauser, S.: Causal semantics of algebraic Petri nets distinguishing concurrency and synchronicity. Fundam. Inform. 86(3), 255–298 (2008)MATHGoogle Scholar
  15. 15.
    Kleijn, J., Koutny, M., Rozenberg, G.: Process semantics for membrane systems. Journal of Automata, Languages and Combinatorics 11(3), 321–340 (2006)MATHMathSciNetGoogle Scholar
  16. 16.
    Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part 1. Theor. Comput. Sci. 13, 85–108 (1981)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Pãun, G.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)MATHCrossRefGoogle Scholar
  18. 18.
    Pinna, G.M., Poigné, A.: On the nature of events: another perspective in concurrency. Theor. Comput. Sci. 138(2), 425–454 (1995)MATHCrossRefGoogle Scholar
  19. 19.
    Pinna, G.M., Saba, A.: An Event Based Semantics of P Systems. Scientific Annals of Computer Science XVIII, 99–127 (2008)Google Scholar
  20. 20.
    Pratt, V.R.: Higher dimensional automata revisited. Mathematical Structures in Computer Science 10(4), 525–548 (2000)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Pratt, V.R.: Transition and cancellation in concurrency and branching time. Mathematical Structures in Computer Science 13(4), 485–529 (2003)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    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 2010

Authors and Affiliations

  • G. Michele Pinna
    • 1
  • Andrea Saba
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariItaly

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