Istituto di Scienza e Tecnologie dell'Informazione     
De Nicola R., Montanari U., Vaandrager F. Back and forth bisimulations. In: CONCUR '90 - Theories of Concurrency: unification and extension. (Amsterdam, August 1990). Proceedings, pp. 152 - 165. J.C.M. Baeten, J.W. Klop (eds.). (Lecture notes in computer science., vol. 458). Springer, 1990.
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 ot branching bisimulation in terms of abstract,on 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.
Subject Bisimulation

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