Equivalences and refinement

  • Rob J. van Glabbeek
  • Ursula Goltz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 469)


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 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.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Rob J. van Glabbeek
    • 1
  • Ursula Goltz
    • 2
  1. 1.Institut für Informatik der TU MünchenMünchen 2
  2. 2.Gesellschaft für Mathematik und DatenverarbeitungSankt Augustin 1

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