Equivalence notions for concurrent systems and refinement of actions

  • Rob van Glabbeek
  • Ursula Goltz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 379)


We investigate equivalence notions for concurrent systems. We consider ”linear time” approaches where the system behaviour is characterised as the set of possible runs as well as ”branching time” approaches where the conflict structure of systems is taken into account. We show that the usual interleaving equivalences, and also the equivalences based on steps (multisets of concurrently executed actions) are not preserved by refinement of atomic actions. We prove that ”linear time” partial order semantics, where causality in runs is explicit, is invariant under refinement. Finally, we consider various bisimulation equivalences based on partial orders and show that the strongest one of them is preserved by refinement whereas the others are not.


Partial Order Linear Time Event Structure Atomic Action Label Transition System 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Rob van Glabbeek
    • 1
  • Ursula Goltz
    • 2
  1. 1.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands
  2. 2.Gesellschaft für Mathematik und DatenverarbeitungSankt Augustin 1German Federal Republic

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