Back and forth bisimulations

  • Rocco De Nicola
  • Ugo Montanari
  • Frits Vaandrager
Selected Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 458)


This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation leads to the same equivalence as the ordinary notion of strong bisimulation. Then it is shown that the back and forth variant of Milner's observation equivalence is different from (and finer than) observation equivalence. In fact we prove that it coincides with the branching bisimulation equivalence of Van Glabbeek & Weijland. Also the back and forth variants of branching, η and delay bisimulation lead to branching bisimulation equivalence. The notion of back and forth bisimulation moreover leads to characterizations of branching bisimulation in terms of abstraction homomorphisms and in terms of Hennessy-Milner logic with backward modalities. In our view these results support the claim that branching bisimulation is a natural and important notion.


Transition System Transfer Property Label Transition System Kripke Structure Satisfaction Relation 
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 1990

Authors and Affiliations

  • Rocco De Nicola
    • 1
  • Ugo Montanari
    • 2
  • Frits Vaandrager
    • 3
  1. 1.Istituto di Elaborazione dell' Informazione, C.N.R.PisaItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaPisaItaly
  3. 3.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands

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