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An algebraic characterization of transition system equivalences. (English) Zbl 0679.68116
From the text: “I. Castellani [1987, J. Comput. Syst. Sci. 34, 210-235 (1987; Zbl 0619.68021)] has shown that observation equivalence of transition systems could be characterized by particular reductions: systems are equivalent if, and only if, they can be reduced to the same form. Moreover, every transition system has a minimal reduced form. We extend these results to logical equivalence, by an algebraic interpretation of temporal logic: we characterize logical equivalence of transition systems by particular reductions (saturating quasi- homomorphisms) of their power algebras of sets of states and paths and prove that every power algebra has a minimal reduced form. We then offer alternative proofs for logical characterizations of observations equivalence: in particular we apply our method to prove M. Hennessy and C. Stirling’s [Lect. Notes Comput. Sci. 176, 301-311 (1984; Zbl 0557.68029)] result that “Future Perfect” logic characterizes observation equivalence of generalized transition systems, i.e. systems whose infinite behaviours are restricted by arbitrary fairness constraints.”
Reviewer: B.Ponděliček

68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
Full Text: DOI
[1] Dicky, A., An algebraic and algorithmic method for analysing transition systems, Theoret. comput. sci., 46, 285-303, (1986) · Zbl 0617.68035
[2] Bloom, S.L.; Troeger, D.R., A logical characterization of observation equivalence, Theoret. comput. sci., 35, 43-53, (1985) · Zbl 0558.68027
[3] Stirling, C., Proof theoretic characterization of observation equivalence, Theoret. comput. sci., 39, 27-45, (1985) · Zbl 0567.68020
[4] Kozen, D., Results on the propositional μ-calculus, Theoret. comput. sci., 27, 333-354, (1984) · Zbl 0553.03007
[5] Park, D., Concurrency and automata on infinite sequence, (), 167-183
[6] Hennessy, M.; Milner, R., Algebraic laws for nondeterminism and concurrency, J. assoc. comput. Mach., 32, 137-161, (1985) · Zbl 0629.68021
[7] Hennessy, M.; Stirling, C., The power of the future perfect in program logics, (), 301-311 · Zbl 0557.68029
[8] Castellani, I., Bisimulations and abstraction homomorphisms, J. comput. system sci., 34, 210-235, (1987) · Zbl 0619.68021
[9] Sifakis, J., Property-preserving homomorphisms of transition systems, (), 458-473
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