R. v. Glabbeek, S. Smolka, B. Steffen, and C. Tofts. Reactive, generative and stratified models of probabilistic processes. IEEE Symposium on Logic in Computer Science, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(ff; f 1 ) ff; f 2 ) do not appear in the metric model, and thus this type of over specification will be eliminated, therefore preventing the definite loss of any full abstraction result. Note that a similar condition was required for the probabilistic case [11] since in the terminology of [16] a reactive model was being considered. Definition 5.1 Let X D . X is said to satisfy the reactiveness condition if, for any p; q 2 D , where p = ff; f) and q = ff; g) if p; q 2 X then it must be the case that either ff 6= ff or p = q. Then let P r denote the powerset operator ....

R.J.van Glabbeek, S.A.Smolka, B.Steffen and C.Tofts. Reactive, generative and stratified models of probabilistic processes, Proc. Concur'92, LNCS, 630, Springer, 1992.

....the message will arrive. Similarly, one can be interested not only in the fact that the message arrives, but also in the fact that it arrives (with a certain probability, say 1 Gamma ffl) before an amount of time t has passed. Therefore, several timed (e.g. 29, 2, 26, 18] probabilistic (e.g. [32, 3, 28, 27, 9]) and timed probabilistic (e.g. 15, 24, 13] extensions of process algebras have been proposed in the literature. Nevertheless, in timed process algebras time information was mainly specified in two different forms: either by adding a delay operator or by including information about the time ....

R. van Glabbeek, S. A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59--80, 1995.

....#w P # indicates that process P is willing to perform action # with probability p and then behave as process P # . Auxiliary strings W are introduced as a technical means to distinguish transitions (of a process like a.0 1 2 a. 0) that would otherwise be indistinguishable (see also for instance [5], 4] We will write P # # # if there are no p # [0, 1] Q #Pand w # W such that P #,p #w Q. We will also write P ## if for each # # Act, P # # and we will write P # if not P ##. In the rules for choice, parallel composition and restriction, we use normalization factors. ....

....for choice, parallel composition and restriction, we use normalization factors. These normalization factors are used to ensure that the defined process is either stochastic or contains no transitions at all. A process is called stochastic if the sum of the probabilities of its transitions is 1 [5]. Except for restriction, all inference rules in Figure 1 preserve the property of stochasticity. In case of restriction, the defined process may not have any transitions at all. The transition rules in Figure 1 are such that a process has no transitions with probability 0. The normalization ....

R. van Glabbeek, S.A. Smolka and B. Ste#en, Reactive, generative and stratified models of probabilistic processes, Information and Computation, 121(1), pp. 59--80, 1995.

....algebras is obvious in order to perform a more qualitative analysis of concurrent distributed systems which deal with statistical and probabilistic phenomena, such as random algorithms and failure rates in a communication channel. Several models introduce probabilities into process algebras. In [7], three different models are presented (reactive, generative, and stratified) and semantics are defined using bisimulation. Inside the testing framework, there are also several proposals for probabilistic process algebras. Some of them use tests without probabilistic information (e.g. 1,2,12,10] ....

R. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59--80, 1995.

....0 (h( Omega 1 ) P( Omega 0 ) P 0 (f gjh( Omega 1 ) 6. The precategory of generative discrete probabilistic automata We now provide the above mentioned universal characterization of the aggregation, interconnection, and restriction of generative probabilistic automata. As discussed in van Glabeek et al. 1995), the latter constitute a more general model than the classical reactive model Rabin (1963) since, in addition to the relative probabilities of transitions under the same action, they contain information about the relative probabilities of transitions under different actions. For further details ....

....model than the classical reactive model Rabin (1963) since, in addition to the relative probabilities of transitions under the same action, they contain information about the relative probabilities of transitions under different actions. For further details and comparisons of these models see van Glabeek et al. 1995). Generative probabilistic automata are used as a semantic model of probabilistic concurrent programs (van Glabeek et al. 1995) and, in the more restrictive form of (a simplified type of) decision trees, in machine learning and knowledge representation (Pinto et al. 1999) L. Schroder and P. ....

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Van Glabeek, R., Smolka, S., Steffen, B. and Tofts, C. (1995) Reactive, generative and stratified models for probabilistic processes. Information and Computation 121 (1), 59--80.

....algebras is obvious in order to perform a more qualitative analysis of concurrent distributed systems which manage with statistical and probabilistic phenomena, such as random algorithms or failure rates in a communication channel. Several models introduce probabilities into process algebras. In [vGSS95] models are classified with respect to the interpretation of probabilities, by using (strong) bisimulation. Inside the testing framework, there are also several proposals for probabilistic process algebras (e.g. Chr90, CSZ92, YL92, NdFL95, NdF95] In the present paper the underlying semantic ....

....in the parallel operators only influence the probability with which a probabilistic transition is executed, we have preferred to consider a parallel operator, inherited from CSP, without any probabilistic parameter. More difficult than defining probabilistic operators is assigning semantics. In [vGSS95] the reactive, generative, and stratified models are described and studied in the framework of probabilistic (strong) bisimulation. In the generative model there exists a unique probability distribution relating all actions, in contrast with the reactive model where there exists a probability ....

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R. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59--80, 1995.

....process algebras have tried to close the gap between formal models and real systems. In particular, features which were abstracted before have been introduced in these models. This is the case of probabilistic information. Several models have introduced probabilities into process algebras, and in [22] models are classified with respect to the interpretation of probabilities in three groups: reactive, generative, and stratified. In the reactive model there is a different probability distribution for every action, that is, there is no probabilistic relation between different actions. In the ....

R. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59--80, 1995.

....cross over composition yields an automatic technique for transforming a protocol, designed and proved for a fair scheduler, into an equivalent protocol for an unfair scheduler, making simpler the task of the designer prover. 1. 1 Others related works Probabilistic I O automata were presented in [23] and [7] This work was improved by Wu, Smolka and Stark [25] In [22] Lynch and Segala introduced a method including the adversary in the probabilistic automaton which models a distributed system. They made a distinction between the protocol which is probabilistic and the adversary which is non ....

R.J. van Glabbeek, S.A. Smolka, B. Steffen, and C.M.N. Toft. Reactive, generative and stratified models of probabilistic processes. In Proceedings 5th Annual Symposium on Logic in Computer Science, Philadelphia, USA, 1990.

....laws based on a notion of strong bisimulation. 1 Introduction In this paper we present a fully parallel calculus of synchronizing processes. The calculus was originally designed as a first step towards a probabilistic one [11] Several probabilistic models have been proposed in the literature [2, 4, 5, 6, 8, 13, 18, 21, 22]. They are derived mostly from SCCS [15] which, contrary to CCS [14] has a noninterleaving semantics. In fact, in order to reason about probabilistic systems, it is a crucial point to have a direct correspondence between choice operators in behaviour expressions and the branching structure of ....

R. van Glabbeek, S.A. Smolka, B. Steffen, C. Tofts. Reactive, Generative and Stratified Models of Probabilistic Processes. Proc. of 5th LICS, 1990.

....which set of events to offer the environment. The difference is not in who makes the probabilistic choice (it is always the process) rather it is in who decides the set from which the choice will be made. Our work belongs to the second group. In the first group we find the generative model of [16] and the extended failures model of [10] the first is CCS [11] and the second CSPbased. In the generative model (but using our syntax) a probabilistic external choice a A p [ b B selects the left branch if the environment offers only a, and similarly the right if b. When both a; b are ....

....Ours is that two processes are equal when the test (F ) yields identical results for all finite F . The (F ) equivalence is finer than those based on assigning probabilities to the results of trace like tests, as in [12, 10, 13] and the reactive and generative models of [16]; yet it is coarser than the stratified bisimulation of [16] and the probabilistic bisimulation of [8] If an equivalence is very coarse (identifying many processes) then some operators will not be definable (or, alternatively expressed, in the presence of those operators the equivalence ....

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R.J. van Glabbeek, S.A. Smolka, B. Steffen, and C. Tofts. Reactive, generative and stratified models of probabilistic processes. In IEEE Symposium on Logic in Computer Science, Philadelphia, PA, USA, June 1990.

....of probabilistic choices. To adequately reason about such sequences as a whole, distributions are used. The modeling of probability has been the subject of various papers. The usual approach, when dealing with probability, is to replace non deterministic choice by probabilistic choice. In [17], 28] and [3] this approach is followed. However, interpreting all choices as probabilistic choices does not seem to be appropriate, especially when there is also parallel composition. When replacing non deterministic choice with probabilistic choice, parallel composition will either become ....

....sections 5 and 6 have at least the same expressibility as the probabilistic automata used in [27] In [27] these probabilistic automata are the starting point of the discussion whereas in this report, constructing the transition system for a statement in the language is also an important step. In [17] reactive, generative and stratified models are given for a calculus PCCS . In this calculus, based on Milner s SCCS [24] the non deterministic choice has been replaced by probabilistic choice and the parallel composition is a synchronous product. The different semantics are given using SOS and ....

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R.J. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121:59--80, 1995.

....of probabilistic and nondeterministic choice is studied in the context of two process languages, a nonconcurrent and a concurrent one. Various operational, denotational and axiomatic models are proposed in the literature to describe the probabilistic operator of PCCS (cf. 7] See, e.g. [14, 17, 18, 8, 21, 16]. Often the nondeterminacy is removed or restricted when treating probability, and the parallel operator is interpreted as a synchronous product. In a number of these references, though, both probability on the one hand, and nondeterminism and or concurrency on the other are treated on equal ....

....choice comes equipped with. This leads to different meanings for a Phi 1=2 fail and a Phi 1=2 (fail2fail) for example. Here the operator Phi 1=2 denotes a probabilistic choice taking both the left and right operand with probability 1=2. For the probabilistic choice there are, as coined in [8], the interpretations of reactive, generative and stratified probability. We have chosen to deal with a stratified model as it is the most general one. We expect no difficulties for the translation of the semantical models to, e.g. the generative setting. As a consequence the process languages ....

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R.J. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121:59--80, 1995.

....the model used for performance evaluation guarantees the correspondence between the system and the performance model by construction. In the literature there have been many attempts to extend models of concurrency with quantitative information (e.g. temporal [31] or probabilistic extensions [37, 20, 25]) but the most promising approach is the one based on stochastic extensions. The first results appeared in the field of Petri nets with their stochastic extensions [35, 29, 2, 17, 26] Only in the last years stochastic extensions of process algebras [18, 23, 4, 10] have been considered to ....

R.J. van Glabbeek, S.A. Smolka, B. Steffen, and C.M.N. Tofts. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 1995.

....this approach in the area of probabilistic languages, but so far no framework encompassing the three semantics has been proposed for a probabilistic extension of a process algebra. In this paper we consider a probabilistic variant of a process algebra (a reactive language in the terminology of [20]) based on CCS [17] and CSP [8] The calculus contains recursion, deterministic choice and concurrency, but instead of non deterministic choice it has (action guarded) probabilistic choice. The operational semantics of this language is given in terms of the probabilistic transition systems and ....

....in this area has focussed mainly on the operational side, see e. g [2, 4, 6, 10, 12, 15, 19, 21] In [2, 12, 15, 19] complete axiomatizations of the constructed probabilistic process calculi are given, with [15] dealing with a reactive model and [2, 12] generative models in the terminology of [20]. The probabilistic powerdomain construction [9] has been applied to give domain theoretic semantics to certain languages, but as yet no fully abstract metric model has been proposed. Fully abstract characterizations for testing equivalences are included in [11, 4, 21] denotational semantics is ....

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R.J.van Glabbeek, S.A.Smolka, B.Steffen and C.Tofts. Reactive, generative and stratified models of probabilistic processes, Proc. Concur'92, LNCS, 630, Springer, 1992.

....is constructed. These combinators can be used to compose specifications from simple ones. Thus, we can specify and analyze a complex system in terms of the specifications of its components. To reason about probabilistic processes, several probabilistic process calculi have been developed [C90] [GSST90] [HJ90] JS90] LS91] BBS92] L93] by extending traditional process calculi like CCS and CSP with a stochastic choice operator P ffi [p i ]E i . Intuitively, P ffi [p i ]E i describes a process that may become E i with probability p i . This requires that the probability distribution on the ....

....laws are developed in terms of the simulations and associated equivalences, including an expansion theorem for parallel composition. They provide a complete axiomatization for the induced congruence by . Over the past few years, a number of probabilistic models have been developed, e.g. C90] [GSST90] [HJ90] JS90] LS91] BBS92] L93] As said earlier, all these work assume that the probability for a probabilistic transition is completely known. In [JL91] Larsen and Jonsson proposed a different model named probabilistic specification system, which allows intervals (more generally sets) of ....

R. van Glabbeek, S. A. Smolka, B. Steffen and C. Tofts, Reactive, Generative and Stratified Models of Probabilistic Processes, in the Proc. of LICS'90, 1990.

....functional analysis. A unique framework for the two kinds of analyses goes towards the definition of an integrated environment for the development of complex systems. The literature presents some attempts to include into process algebras quantitative information such as time [23] and probabilities [35, 17, 12] for performance evaluation, but the most promising one are based on the so called stochastic process algebras [11, 14, 3, 4] They enrich the actions of classical calculi with probabilistic distributions, yielding prefixes like (a; F ) The actual firing of an action enabled occurs after a delay ....

R.J. van Glabbeek, S.A. Smolka, B. Steffen, and C.M.N. Tofts. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 1995.

....laws that form a sound and complete axiomatization and elucidates the special algebraic properties of our calculus. Section 5 presents a brief summary and describes directions for further investigations. Related Work The calculus we present here is strongly influenced by PCCS [GJS90] In [vGSST90] different types of semantics for PCCS are studied and related to each other in terms of bisimulation based on [LS89] A complete axiomatization of PCCS has been presented in [JS90] In [GHR93] the expressive power of TIPP, a language based on MPA, is studied by means of several examples. ....

R. van Glabbeek, S.A. Smolka, B. Steffen, and C.M.N. Tofts. Reactive, Generative and Stratified Models of Probabilistic Processes. In Proceedings of 5th Anual IEEE Symposium on Logic in Computer Science, pages 130-- 141, Philadelphia, PA, June 1990.

....three equivalences based on testing and gives three denotational models; he then shows each of his denotational models to be fully abstract with respect to one of the equivalences. Jou and Smolka consider a number of equivalence relations and show which are refinements of others. Glabbeek et al. [vGSST90] discuss reactive, generative and stratified models of probabilistic processes. 12 CONCLUSIONS 53 ffl They define a reactive model to be one where the environment may only offer one event at a time. If the process can perform the offered event then it makes an internal state transition according ....

R. J. van Glabbeek, S. A. Smolka, B. Steffen, and C. Tofts. Reactive, generative and stratified models of probabilistic processes. In IEEE Symposium on Logic in

....related to bisimulation [6] and has many useful properties: it has a logical characterization in terms of the Hennessy Milner logic [19] see also [8] has an efficient (polynomial) decision procedure [2] and is a congruence for typical process operators. For example, van Glabbeek et al. [11] show that probabilistic bisimulation is a congruence This is a preliminary version. The final version can be accessed at URL: http: www.elsevier.nl locate entcs volume16.html Kwiatkowska and Norman over their calculus PCCS (which contains all the usual SCCS operators) and Baier and ....

R.J. van Glabbeek, S.A. Smolka, B. Steffen and C.M.N. Tofts. Reactive, generative and stratified models of probabilistic processes. In Proc. 5th IEEE Int. Symp. on Logic in Computer Science (LICS), pages 130-141, 1990.

....4. However, a corresponding analysis could be applied to any similar process algebra. Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes 3 tional in nature. We briefly review here what we believe to be some of the more important contributions. Van Glabbeek et al. [vGSST90] discuss reactive, generative and stratified models of probabilistic processes. ffl They define a reactive model to be one where the environment may only offer one event at a time. If the process can perform the offered event then it makes an internal state transition according to some ....

...., etc) In action states, the process offers the environment a choice between a number of different actions; after performing an action, the process evolves into a probabilistic state. The environment is only allowed to offer one action at a time, so this is a reactive model in the terminology of [vGSST90]. In probabilistic states, processes evolve into action states according to some probability distribution. Thus, he differentiates between external and probabilistic choice. In these works we can identify two different sorts of probabilistic branching which we term internal and external. ffl With ....

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R. J. van Glabbeek, S. A. Smolka, B. Steffen, and C. Tofts. Reactive, generative and stratified models of probabilistic processes. In IEEE Symposium on Logic in Computer Science, 1990.

....the probability of occurrence of an undesirable event. We illustrate PACSR specification and analysis by means of a telecommunications example. 1 Introduction Process algebras such as CCS [15] have proved to be effective for specification and analysis of distributed systems. Numerous real time [22, 16, 12] and probabilistic [20] extensions of process algebras exist. We propose an approach that allows one to perform probabilistic analysis for real time systems. A common high level view of a distributed real time system is that its components compete for access to shared resources, communicating with ....

R. J. van Glabbeek, S. A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59--80, 15 Aug. 1995.

....for the Demos language compared with that of the CCS semantics. This results for the ability to construct compound atomic actions in SCCS and suggests that further more detailed studies of general simulation systems should be undertaken in formal languages with this degree of expressiveness [vGSST90, Tof90a, CW90, Tof94]. Equally it will be interesting to compare the effectiveness of other more expressive process algebras (such as [MT90, Han92] at expressing the temporal or probabilistic properties of simulations. Acknowledgements The material presented here has been under development some time and has ....

R. von Glabbeek, S. Smolka, B. Steffen and C. Tofts, Reactive, Generative and Stratified Models of Probabilistic Processes, in proceedings LICS '90.

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R. v. Glabbeek, S. Smolka, B. Steffen, and C. Tofts. Reactive, generative and stratified models of probabilistic processes. IEEE Symposium on Logic in Computer Science, 1990.

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Glabbeek, R. J. van, S. A. Smolka, and B. Ste#en. Reactive, Generative and Stratified Models of Probabilistic Processes, Information and Computation 121:59--80, 1995.

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R.J.van Glabbeek, S.A. Smolka, B. Steffen and C. Tofts. Reactive, generative and stratified models of probabilistic processes, Proc. 5th IEEE Int. Symp. on Logic in Computer Science (LICS), pages 130-141, 1990.

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