Abstract
We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three Hennessy-Milner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only in the kind of diamond operator used. Compared to the Larsen and Skou logic for reactive systems, these logics introduce a new operator that measures the probability of the set of states that satisfy a formula. Moreover, the satisfaction relation is defined on measures rather than single states.
We rederive previous results of Desharnais et al. by defining sublogics for Reactive and Alternating Models viewed as restrictions of probabilistic automata. Finally, we identify restrictions on probabilistic automata, weaker than those imposed by the Alternating Models, that preserve the logical characterization of Desharnais et al. These restrictions require that each state either enables several ordinary transitions or enables a single probabilistic transition.
Supported by INRIA project ProNoBiS and MIUR project AIDA.
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Bravetti, M., D’Argenio, P.R.: Tutte le algebre insieme: Concepts, discussions and relations of stochastic process algebras with general distributions. In: Baier, C., et al. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 44–88. Springer, Heidelberg (2004)
Cattani, S., Segala, R.: Decision algorithms for probabilistic bisimulation. In: Brim, L., et al. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 371–385. Springer, Heidelberg (2002)
Deng, Y.: Axiomatisations and Types for Probabilistic and Mobile Processes. PhD thesis, Ecole des Mines de Paris (2005)
Desharnais, J., Edalat, A., Panangaden, P.: A logical chracterization of bisimulation for labelled markov processes. In: Proceedings of the 13th IEEE Symposium On Logic In Computer Science, pp. 478–489 (1998)
Desharnais, J., et al.: Weak bisimulation is sound and complete for PCTL. In: Brim, L., et al. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 355–370. Springer, Heidelberg (2002)
van Glabbeek, R.J., et al.: Reactive, generative, and stratified models of probabilistic processes. In: Proceedings 5th Annual Symposium on Logic in Computer Science, Philadelphia, USA, pp. 130–141. IEEE Computer Society Press, Los Alamitos (1990)
Hansson, H.: Time and Probability in Formal Design of Distributed Systems. PhD thesis, Department of Computer Science, Uppsala University (1991)
Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of the ACM 32(1), 137–161 (1985)
Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Proceedings of the 6th IEEE Symposium on Logic in Computer Science, Amsterdam, July 1991, pp. 266–277 (1991)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94(1), 1–28 (1991)
Philippou, A., Lee, I., Sokolsky, O.: Weak bisimulation for probabilistic systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 334–349. Springer, Heidelberg (2000)
Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, Dept. of Electrical Engineering and Computer Science, Also appears as technical report MIT/LCS/TR-676 (1995)
Segala, R.: Probability and nondeterminism in operational models for concurrency. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 64–78. Springer, Heidelberg (2006)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (1995)
Segala, R., Turrini, A.: Comparative analysis of bisimulation relations on alternating and non-alternating probabilistic models. In: Proceedings of QEST 2005 (September 2005)
Sokolova, A., de Vink, E.P.: Probabilistic automata: system types, parallel composition and comparison. In: Baier, C., et al. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 1–43. Springer, Heidelberg (2004)
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Parma, A., Segala, R. (2007). Logical Characterizations of Bisimulations for Discrete Probabilistic Systems. In: Seidl, H. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2007. Lecture Notes in Computer Science, vol 4423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71389-0_21
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DOI: https://doi.org/10.1007/978-3-540-71389-0_21
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