Abstract
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.
First and second authors where supported by ESPRIT project 3011 (CEDISYS). The research of the third author was supported by RACE project no. 1046, Specification and Programming Environment for Communication Software (SPECS) and by ESPRIT project no. 3006 (CONCUR).
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References
P. Aczel (1988): Non-well-founded sets, CSLI Lecture Notes No.14, Stanford University.
A. Arnold & A. Dicky (1989): An algebraic characterization of transition system equivalences. Information and Computation 82, pp. 198–229.
J.C.M. Baeten & R.J. van Glabbeek (1987): Another look at abstraction in process algebra. In: Proceedings ICALP 87, Karlsruhe (Th. Ottman, ed.), LNCS 267, Springer-Verlag, pp. 84–94.
M.C. Browne, E.M. Clarke & O. Grumberg (1988): Characterizing finite Kripke structures in propositional temporal logic. Theoretical Computer Science 59(1,2), pp. 115–131.
I. Castellani (1987): Bisimulations and abstraction homomorphisms. Journal of Computer and System Sciences 34, pp. 210–235.
I. Castellani, P. Franceschi & U. Montanari (1983): Labeled event structures: a model for observable concurrency. In: Proceedings IFIP TC2 Working Conference on Formal Description of Programming Concepts — II, Garmisch (D. Bjørner, ed.), North-Holland, pp. 383–400.
R. De Nicola & F.W. Vaandrager (1990): Three logics for branching bisimulation (extended abstract). In: Proceedings 5th Annual Symposium on Logic in Computer Science (LICS 90), Philadelphia, USA, IEEE Computer Society Press, Los Alamitos, CA, pp. 118–129, full version to appear as CWI Report CS-R9012.
E.A. Emerson & J.Y. Halpern (1986): 'sometimes’ and ‘Not Never’ revisited: on branching time versus linear time temporal logic. JACM 33(1), pp. 151–178.
R.J. van Glabbeek & W. P. Weijland (1989): Branching time and abstraction in bisimulation semantics (extended abstract). In: Information Processing 89 (G.X. Ritter, ed.), Elsevier Science Publishers B.V. (North Holland), pp. 613–618.
M. Hennessy & R. Milner (1985): Algebraic laws for nondeterminism and concurrency. JACM 32(1), pp. 137–161.
M. Hennessy & C. Stirling (1985): The power of the future perfect in program logics. Information and Control 67, pp. 23–52.
R. Milner (1980): A Calculus of Communicating Systems, LNCS 92, Springer-Verlag.
R. Milner (1981): Modal characterisation of observable machine behaviour. In: Proceedings CAAP 81 (G. Astesiano & C. Bohm, eds.), LNCS 112, Springer-Verlag, pp. 25–34.
R. Milner (1983): Calculi for synchrony and asynchrony. Theoretical Computer Science 25, pp. 267–310.
R. Milner (1989): Communication and concurrency, Prentice-Hall International.
U. Montanari & M. Sgamma (1989): Canonical representatives for observational equivalence classes. In: Resolution Of Equations In Algebraic Structures, Vol. I, Algebraic Techniques (H. Aït-Kaci & M. Nivat, eds.), Academic Press, pp. 293–319.
R. Paige & R. Tarjan (1987): Three partition refinement algorithms. SIAM Journal on Computing 16(6), pp. 973–989.
D.M.R. Park (1981): Concurrency and automata on infinite sequences. In: Proceedings 5th GI Conference (P. Deussen, ed.), LNCS 104, Springer-Verlag, pp. 167–183.
J. Sifakis (1984): Property-preserving homomorphisms of transition systems. In: Proceedings Logics of Programs, 1983 (E. Clarke & D. Kozen, eds.), LNCS 164, Springer-Verlag, pp. 458–473.
C. Stirling (1990): Modal and temporal logics. In: Handbook of Logic in Computer Science, Vol I (S. Abramsky, ed.), to appear.
W.P. Weijland (1989): Synchrony and asynchrony in process algebra. Ph.D. Thesis, University of Amsterdam.
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De Nicola, R., Montanari, U., Vaandrager, F. (1990). Back and forth bisimulations. In: Baeten, J.C.M., Klop, J.W. (eds) CONCUR '90 Theories of Concurrency: Unification and Extension. CONCUR 1990. Lecture Notes in Computer Science, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039058
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DOI: https://doi.org/10.1007/BFb0039058
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