Denotational, causal, and operational determinism in event structures

  • Arend Rensink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1059)


Determinism of labelled transition systems and trees is a concept of theoretical and practical importance. We study its generalisation to event structures. It turns out that the result depends on what characterising property of tree determinism one sets out to generalise. We present three distinct notions of event structure determinism, and show that none of them shares all the pleasant properties of the one concept for trees.


behavioural models event structures concurrent languages determinism partial order models trees 


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  1. 1.
    P. Darondeau and P. Degano. Causal trees=interleaving+ causality. In Guessarian, ed., Semantics of Systems of Concurrent Processes, vol. 469 of LNCS, pp. 239–255. Springer, 1990.Google Scholar
  2. 2.
    J. Engelfriet. Branching processes of Petri nets. Acta Inf., 28:575–591, 1991.Google Scholar
  3. 3.
    J. Meseguer, U. Montanari, and V. Sassone. On the semantics of Petri nets. In W. R. Cleaveland, ed., Concur '92, vol. 630 of LNCS, pp. 286–301. Springer, 1992.Google Scholar
  4. 4.
    M. Nielsen, G. D. Plotkin, and G. Winskel. Petri nets, event structures and domains, part 1. Theoretical Comput. Sci., 13:85–108, 1981.Google Scholar
  5. 5.
    M. Nielsen, V. Sassone, and G. Winskel. Relationships between models for concurrency. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, eds., A Decade of Concurrency, vol. 803 of LNCS, pp. 425–476. Springer, 1994.Google Scholar
  6. 6.
    A. Rensink. Deterministic pomsets. Hildesheimer Informatik-Berichte 94/30, UniversitÄt Hildesheim, Nov. 1994.Google Scholar
  7. 7.
    A. Rensink. A complete theory of deterministic event structures. In I. Lee and S. A. Smolka, eds., Concur '95: Concurrency Theory, vol. 962 of LNCS, pp. 160–174. Springer, 1995.Google Scholar
  8. 8.
    A. Rensink. Denotational, causal, and operational determinism in event structures. Hildesheimer Informatik-Berichte 95/29, UniversitÄt Hildesheim, Sept. 1995.Google Scholar
  9. 9.
    A. Rensink. Further deterministic behavioural models for concurrency. Hildesheimer Informatik-Berichte 95/30, UniversitÄt Hildesheim, Oct. 1995.Google Scholar
  10. 10.
    V. Sassone. On the Semantics of Petri Nets: Processes, Unfoldings and Infinite Computations. PhD thesis, Universitá de Pisa, Mar. 1994. Available as TD-6/94.Google Scholar
  11. 11.
    V. Sassone, M. Nielsen, and G. Winskel. A classification of models for concurrency. In E. Best, ed., Concur '93, vol. 715 of LNCS, pp. 82–96. Springer, 1993.Google Scholar
  12. 12.
    V. Sassone, M. Nielsen, and G. Winskel. Deterministic behavioural models for concurrency. In A. M. Borzyszkowski and S. Sokołowski, eds., Mathematical Foundations of Computer Science 1993, vol. 711 of LNCS, pp. 682–692. Springer, 1993.Google Scholar
  13. 13.
    F. W. Vaandrager. Determinism → (event 2structure isomorphism = step sequence equivalence). Theoretical Comput. Sci., 79:275–294, 1991.Google Scholar
  14. 14.
    G. Winskel. Event structures. In W. Brauer, W. Reisig, and G. Rozenberg, eds., Petri Nets: Applications and Relationships to Other Models of Concurrency, vol. 255 of LNCS, pp. 325–392. Springer, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Arend Rensink
    • 1
  1. 1.Institut für InformatikUniversity of HildesheimHildesheim

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