Abstract
This paper offers a complete inference system for branching bisimulation congruence on a basic sublanguage of CCS for representing regular processes with silent moves. Moreover, complete axiomatizations are provided for the guarded expressions in this language, representing the divergence-free processes, and for the recursion-free expressions, representing the finite processes. Furthermore it is argued that in abstract interleaving semantics (at least for finite processes) branching bisimulation congruence is the finest reasonable congruence possible. The argument is that for closed recursion-free process expressions, in the presence of some standard process algebra operations like partially synchronous parallel composition and relabelling, branching bisimulation congruence is completely axiomatized by the usual axioms for strong congruence together with Milner's first τ-law aτ X=aX.
This work was supported by ONR under grant number N00014-92-J-1974.
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References
J.A. Bergstra & J.W. Klop (1985): Algebra of communicating processes with abstraction. Theoretical Computer Science 37(1), pp. 77–121.
J.A. Bergstra & J.W. Klop (1988): A complete inference system for regular processes with silent moves. In F.R. Drake & J.K. Truss, editors: Proceedings Logic Colloquium 1986, Hull, North-Holland, pp. 21–81. First appeared as: Report CS-R8420, CWI, Amsterdam, 1984.
R.J. van Glabbeek (1990): The linear time — branching time spectrum. In J.C.M. Baeten & J.W. Klop, editors: Proceedings CONCUR 90, Amsterdam, LNCS 458, pp. 278–297.
R.J. van Glabbeek & W.P. Weijland (1990): Branching time and abstraction in bisimulation semantics. Technical Report TUM-I9052, SFB-Bericht Nr. 342/29/90 A, Institut für Informatik, Technische Universität München, Munich, Germany. Extended abstract in G.X. Ritter, editor: Information Processing 89, Proceedings of the IFIP 11th World Computer Congress, San Fransisco, USA 1989, Elsevier Science Publishers B.V. (North-Holland), 1989, pp. 613–618.
R. Milner (1984): A complete inference system for a class of regular behaviours. Journal of Computer and System Sciences 28, pp. 439–466.
R. Milner (1989): A complete axiomatisation for observational congruence of finite-state behaviours. Information and Computation 81, pp. 227–247.
R. Milner (1990): Operational and algebraic semantics of concurrent processes. In J. van Leeuwen, editor: Handbook of Theoretical Computer Science, chapter 19, Elsevier Science Publishers B.V. (North-Holland), pp. 1201–1242. Alternatively see Communication and Concurrency, Prentice-Hall International, Englewood Cliffs, 1989, of which an earlier version appeared as A Calculus of Communicating Systems, LNCS 92, Springer-Verlag, 1980.
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van Glabbeek, R.J. (1993). A complete axiomatization for branching bisimulation congruence of finite-state behaviours. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_39
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DOI: https://doi.org/10.1007/3-540-57182-5_39
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