J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. Inf. Comput., 179(2):163-- 193, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....demonic product of two transition kernels, or probabilistic relations, as we will also call them, it proposes a de nition for this product, and it investigates two properties, viz. stability under bisimulation and the behavior of an associated set theoretic relation. Two notions of bisimulations [DEP98, Rut96] are de ned for transition kernels, and it is shown that they are very closely related. Then we show that bisimililarity is preserved through the ordinary, and through the demonic product: if the factors are bisimilar, and if the bisimulation is related through a probabilistic object, so are the ....

....thus real valued functions on a Polish space are captured by Observation 10. In what follows, bisimulation will mean 2 bisimulation; we write O 1 hA;Ki O 2 if hA; Ki is a bisimulation for O 1 and O 2 . The Demonic Product of Probabilistic Relations Remarks: 1. Desharnais, Edalat and Panangaden [DEP98] de ne bisimulations between labelled Markov processes as spans of zig zag morphisms in the category A of analytic spaces. They work in the full subcategory of 1l A # S that has objects of the diagonal form hS; S; Ki. Because the product of two analytic spaces is an analytic space again [Par67, ....

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J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation of labelled markovprocesses. Technical report, School of Computer Science, McGill University, Montreal, 1998.

....of probabilistic systems. Finally, we would like to mention the work on probabilistic process algebras (e.g. 4,31,68,7] for an overview see [38] which covers areas like probabilistic bisimulation [46,18] veri cation of probabilistic systems [5,33] and semantics of probabilistic systems [10,55,42]. 7 Conclusions and Further Work In this paper we have presented a generic approach to a denotational semantics for probabilistic concurrent languages which is based on linear structures. We have shown that linear operators, or more abstractly C algebras, constitute an appropriate semantical ....

Blute, R., J. Desharnais, A. Edalat and P. Panangaden, Bisimulation for labelled Markov processes, in: Proceedings, Twelth Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, Warsaw, Poland, 1997, pp. 149-158.

....the uniform coalgebraic treatment helps to clarify the picture and to organize the setting. In earlier work comparison is made between a number of probabilistic process equivalences (see, e.g. GSS95] and categorical formulations of LarsenSkou bisimulation and stochastic bisimulation are given [DEP02,VR99]. In recent work [BSV02] we focused on the relationship between these and various related notions and made a taxonomy of the most prominent types of probabilistic bisimulation. There the coalgebraic framework proved useful already for a unified presentation of the diverse types of systems. In the ....

J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for Labelled Markov Processes. Information and Computation, 179:163--193, 2002.

.... captures the strong bisimulation relation of Milner [10] Subsequently in [3] it was shown that abstract bisimilarity can also capture Hennessy s testing equivalences [5] Milner and Sangiorgi s barbed bisimulation [11] and Larsen and Skou s probabilistic bisimulation [9] More recently, in [2], a bisimulation relation for Markov processes on Polish spaces was formulated in this categorical framework, extending the work of Larsen and Skou. Other attempts to formulate the notion of bisimulation in categorical language, include the coalgebraic approach of [6, 13] All this evidence ....

R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled markov processes. In Logic in Computer Science, pages 149--158. IEEE Press, 1997.

....uniform coalgebraic treatment helps to clarify the picture and to organize the setting. In earlier work comparison is made between a number of probabilistic process equivalences (see, e.g. GSS95] Categorial formulations of Larsen Skou bisimulation and stochastic bisimulation are advocated in [DEP02,VR99]. In recent work we focused on the relationships between these and various related notions and made a taxonomy of the most prominent notions of probabilistic bisimulation. The coalgebraic framework proved useful already in [BSV02] for a unified presentation of the diverse types of systems. In the ....

J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for Labelled Markov Processes. Information and Computation, 179:163--193, 2002.

.... captures the strong bisimulation relation of Milner [13] Subsequently in [3] it was shown that abstract bisimilarity can also capture Hennessy s testing equivalences [4] Milner and Sangiorgi s barbed bisimulation [14] and Larsen and Skou s probabilistic bisimulation [11] More recently, in [2], Blute et al. formulated a bisimulation relation for Markov processes on Polish spaces in this categorical framework, extending the work of Larsen and Skou. All this evidence further attests to the suitability of this abstract definition as an appropriate venue for formulation of bisimilarity ....

R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled markov processes. In Logic in Computer Science, pages 149-158. IEEE Press, 1997.

.... captures the strong bisimulation relation of Milner [10] Subsequently in [4] it was shown that abstract bisimilarity can also capture Hennessy s testing equivalences [6] Milner and Sangiorgi s barbed bisimulation [11] and Larsen and Skou s probabilistic bisimulation [8] More recently, in [5], Blute et al. formulated a bisimulation relation for Markov processes on Polish spaces in this categorical framework, extending the work of Larsen and Skou. All this evidence further attests to the suitability of this abstract definition as an appropriate venue for formulation of bisimilarity ....

R. Blute et. al. Bisimulation for labelled markov processes. In Logic in Computer Science, pages 149--158. 1997.

....of general function spaces in Prof I . It is left to verify that equations solved in Set I Prof give meaningful solutions Alternatively one might consider enriching over categories of sets with probability distributions on their elements to be able to cope with probabilistic Markov processes [70, 16]. Following suggestions of Martin Hyland, we are also currently investigating the possibility of considering extensions of the category of name sets, This to allow the possibility of having meaningful solutions for equations involving both higher order and name passing features already in Cat ....

Richard Blute, Josee Desharnais, Abbas Edalat, and Prakash Panangaden. Bisimulation for labelled Markov processes. In LICS '97 [75], pages 149--158.

....system is just a special case of a continuous one where the oe algebra is discrete and the transition subprobability measure is determined by a subprobability distribution. Probabilistic bisimulation has been generalized to the continuous setting by Blute, Desharnais, Edalat and Panangaden [7]. Definition 28 An equivalence relation R on the set S of the states of a continuous probabilistic transition system is a probabilistic bisimulation if s 1 R s 2 implies t s1 ;a (B) t s2 ;a (B) for all R closed measurable sets B and a 2 Act . A set B is R closed if s 1 2 B and s 1 R s 2 ....

R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. In Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, pages 149--158, Warsaw, June/July 1997. IEEE.

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R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. In Proceedings of the Twelfth IEEE Symposium On Logic In Computer Science, Warsaw, Poland., 1997.

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Blute, R., Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled Markov processes. In: Proceedings of the Twelfth IEEE Symposium On Logic In Computer Science, Warsaw, Poland. (1997)

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J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. Information and Computation, 179(2):163--193, Dec 2002.

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Blute, R., Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled Markov processes. In: Proceedings of the Twelfth IEEE Symposium On Logic In Computer Science, Warsaw, Poland. (1997)

....with various examples. The following section 7 describes a process algebra of probabilistically determinate processes. We conclude with a section 8 on the asymptotic metric. 2 Background This section on background recalls de nitions from previous work on partial labelled Markov processes [BDEP97, DEP98, LS91] and sets up the basic notations and framework for the rest of the paper. We de ne discrete and continuous processes separately. A reader interested only in the discrete case can safely skip the section on continuous systems though the proofs are usually carried out for the general ....

....paper. Probabilistic bisimulation means matching the moves and probabilities thus each system must be able to make the same transitions with the same probabilities as the other. The de nition that we use is an adaptation of the de nition presented in the previous section. In an earlier paper [BDEP97] we had introduced a version of this de nition based on categorical ideas but in the present paper we use a version much closer in form to that of Larsen and Skou that we introduced in [DGJP00] We also recapitulate the result on logical characterization of bisimulation. Let R be a relation on ....

R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. In Proceedings of the Twelfth IEEE Symposium On Logic In Computer Science, Warsaw, Poland., 1997.

....in particular this includes situations where the state space may be continuous. They are essentially traditional discrete time Markov processes enriched with the process algebra based notion of interaction by synchronization on labels. These have been studied intensively in the last few years ([5 7, 14]) This is because they embody simple probabilistic interactive behaviours, and yet are rich enough to encompass many examples and to suggest interesting mathematics. The initial motivation was the inclusion of continuous state spaces with a view towards eventual applications involving stochastic ....

....#. Both definitions are related by h # (a, s, Q) h(a, Q) s) The functions h, h # are commonly referred to as transition probability functions or Markov kernels (or stochastic kernels) Where denotes an increasing sequence of sets Qn , i.e. for all n, Qn Qn 1 . In previous treatments [5] LMPs were required to have an analytic state space. This was needed for the proof of the logical characterization of bisimulation. We will not mention this again in the present paper since we will not need the analytic structure. In fact it is hard to give examples of spaces that are not ....

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J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. Information and Computation, 179(2):163--193, Dec 2002. Available from http://www.ift.ulaval.ca/~jodesharnais.

....s # t s; the sample paths of W can be chosen to be continuous with probability 1. This mathematical model is the starting point of many stochastic systems; see the book Stochastic Di#erential Equations by ksendal [ks95] for a very readable survey. In a series of previous papers [BDEP97, DEP98, DEP02] we studied Markov processes with continuous state spaces, called labelled Markov processes or LMPs. We gave a definition of bisimulation between LMPs, and gave a logical characterization of this bisimulation. We have also explored the expressiveness and semantics of probabilistic ....

....in the state s before the transition. In general the transition probabilities could depend on time, in the sense that the transition probability could be di#erent at every step, but still independent of past history; we always consider the time independent case. The work was first announced in [BDEP97] We will work with sub probability functions; i.e. with functions where #(s, S) 1 rather than #(s, S) 1. The mathematical results go through in this extended case. We view processes where the transition functions are only sub probabilities as being partially defined, opening the way for a ....

[Article contains additional citation context not shown here]

R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. In Proceedings of the Twelfth IEEE Symposium On Logic In Computer Science, Warsaw, Poland., 1997.

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J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. Inf. Comput., 179(2):163-- 193, 2002.

No context found.

Josee Desharnais, Abbas Edalat, and Prakash Panangaden. Bisimulation for labelled markov processes. Information and Computation, 179(2):163--193, 2002.

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Desharnais, J., Edalat, A., and Panangaden, P. Bisimulation for labelled Markov processes. Information and Computation 179, 2 (2002), 163--193.

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R. Blute, J. Desharnais, A. Edalat, and P. Panangaden, Bisimulation for labelled Markov processes, LICS'97, 1997, pp. 149--158.

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Richard Blute, Josee Desharnais, Abbas Edalat, and Prakash Panangaden. Bisimulation for labelled markov processes. In Proc. 12th LICS, pages 149--158, 1997.

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J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for Labelled Markov Processes. Information and Computation, 179:163--193, 2002.

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Desharnais, J., Edalat, A., and Panangaden, P. Bisimulation for labelled Markov processes. Information and Computation 179, 2 (2002), 163--193.

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J. Desharnais, A. Edalat and P. Panangaden. Bisimulation for Labelled Markov Processes. Information and Computation, 179(2):163--193, 2002.

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Josee Desharnais, Abbas Edalat, and Prakash Panangaden. Bisimulation for labelled markov processes. Information and Computation (formerly Information and Control), 179(2):163--193, December 2002.

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