G. Lowe. Probabilities and Priorities in Timed CSP. PhD thesis, Oxford University Computing Laboratory, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....she gives a semantics in terms of probability measures on the space of in nite traces, but as this rst model raises some problems when de ning the semantics for the external choice operator, she develops a second semantics, using conditional probability measures. On the other hand, Gavin Lowe [Low93a, Low91, Low93b] has also de ned a denotational model covering both internal and external probabilistic behaviour in Timed CSP, but there are several important di erences with our approach, both at the intuitive and at the technical level. The most important di erence is that he maintains a pure (without any ....

Gavin Lowe. Probabilities and Priorities in Timed CSP. Ph. D. Thesis. Oxford, 1993.

....since reliability requirements can be stated in terms of probabilities of desirable or undesirable behaviours, e.g. the reliability of P i in our design can be formulated in terms of a probability of failing to produce an output. A timed probabilistic version of CSP has also been developed [24] but has not been applied to real time fault tolerance. 22 Acknowledgments The authors are grateful to Francis Tam for his contribution on the initial version of this paper and to Simon Gay and Tomasz Janowski for their constructive comments and suggestions on later versions of this paper. ....

G. Lowe. Probabilities and priorities in timed CSP. D.Phil thesis, Oxford University, 1993.

....of a process being in a given state after it has executed a given action. 1 We will use the notation p q to denote a probabilistic choice in which the process has probability of acting like p, and probability 1 of acting like q, where 0 1. 2 approaches such as [7] and [17] that use a process algebra in which probabilistic choice is substituted for nondeterministic choice. Here, and in the next case, the focus is on the probability that the process in question acts like one branch or the other from the choices listed. approaches such as [20, 4, 8] that extend a ....

G. Lowe, \Probabilities and Priorities in Timed CSP," DPhil Thesis, University of Oxford, 1991.

....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 offered, however, the process itself ....

....dimension of comparison is provided by the notion of equivalence. 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 ....

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G. Lowe. Probabilities and priorities in Timed CSP. Technical monograph, Oxford University Computing Laboratory, 1993.

....given any particular outputs, but it is much more likely in the case of two agree calls that the one who called disagree is actually the one who is paying: the conditional probability given the outputs is not the same as the a priori probability. It seems likely that the use of probabilistic CSP [Sei92, Low93] could directly address this issue. This would allow the association of probability values with particular traces. It may be the case that the same definition of anonymity will extend directly to probabilistic models for CSP: that f Gamma1 A (f A (P) P . In a probabilistic model this would ....

G. Lowe, Probabilities and priorities in timed CSP, D.Phil thesis, Oxford, 1993.

....with High but this seems a bit heavy handed. Constructing semantic models for a process algebra to accurately capture the distinction between the various forms of non determinism has proved difficult. A number of probabilistic process algebras have been proposed, for example Morgan [7] and Lowe [6]. These assume that nondeterminism is resolved at the outset and so do not allow for the possibility of delaying choices and making decisions on the basis of observations of how non deterministic choices are resolved at run time . We thus see why it has proved so difficult to model this scenario ....

G. Lowe. Probabilities and Priorities in Timed CSP. D. Phil thesis, Oxford University, 1993.

....rather than just inclusion derives from the view that the set of possible outcomes of a test is abstracted to an interval. Several models for describing probabilistic aspects of transition systems in the form of e.g. Markov chains, Process Algebras, Timed Petri Nets, etc. have been proposed [GJS90, HJ89, HS84, LS91, Low93, Mol82, PZ86, PS89, VW86]. A model containing probabilistic choice and nondeterministic choice as independent concepts is the so called alternating model by Hansson and Jonsson[HJ90] which is essentially the same as the concurrent Markov chain model studied by Vardi [Var85] it can also be seen as a nondeterministic ....

Gavin Lowe. Probabilities and Priorities in Timed CSP. D. Phil thesis, Oxford, 1993.

....peak calling hours. Criteria for a Probabilistic Real Time Model In recent years, there has been growing research on integrating probabilistic and real time verification, and numerous probabilistic real time process algebras, automata, temporal logics, and algorithms have been developed (e.g. [1, 19, 9]) In particular, most of these approaches extend labeled transition systems and automata by allowing probability distributions to be placed on the transitions, corresponding to the probability that the given transition is selected from its parent state. The associated logics give the ....

G. Lowe. Probabilities and Priorities in Timed CSP. PhD thesis, Oxford University, 1993.

....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 choices E i s is completely ....

....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 probabilities. But they did not ....

Gavin Lowe. Probabilities and Priorities in Timed CSP, Ph.D Thesis, Oxford, 1993.

....and tests with the ability to copy give rise to simulation like preorders [Abr87] Apart from the models already mentioned, a number of models for describing probabilistic aspects of transition systems in the form of e.g. Markov chains, Process Algebras, Timed Petri Nets, etc. have been proposed [GJS90, HJ89, HS84, LS91, Low93, Mol82, PZ86, PS89, VW86]. Logics and associated methods for probabilistic systems can be found in e.g. CY88, HJ89, HS84, Koz83, LS91] Several (bi)simulationbased preorders between probabilistic systems have been investigated, e.g. GJS90] Segala and Lynch [SL94] and Wang [Yi94] present simulation based preorders for ....

Gavin Lowe. Probabilities and Priorities in Timed CSP. D. Phil thesis, Oxford, 1993.

....of nondeterminism; for example, the process a Gamma P Gamma a Gamma Q (where the Gamma is an external choice operator that offers the environment a choice between the initial actions of its two arguments) will, after performing an a, nondeterministically act like either P or Q . In my thesis [Low93b] I got round this by assigning probabilities to the different sides of the external choice; for example, if the process a Gamma P 0 :4 Gamma 0 :6 a Gamma Q performs an a, then with probability 40 it will be the one on the left, and with probability 60 it will be the one on the right. ....

....the probability that P performs a trace from A given that the environment is willing to perform the trace y (and nothing else) This allows her to give a semantics to external choice, but unfortunately, it is not possible to give a semantic definition for hiding in this way. In my thesis [Low93b] I gave a semantic model that covered both internal and external probabilistic behaviour in a probabilistic version of Timed CSP. However, as described above, it was necessary to consider prioritized behaviour, and this resulted in a very complicated semantic model. A common theme between these ....

Gavin Lowe. Probabilities and Priorities in Timed CSP. D. Phil thesis, Oxford, 1993.

....for example, the process a Gamma P Gamma a Gamma Q (where the Gamma is an external choice operator that offers the environment a choice between the initial actions of its two arguments) will, after performing an a, nondeterministically act like either P or Q . In my thesis [Low93b] I got round this by assigning probabilities to the different sides of the external choice; for example, if the process a Gamma P 0 :4 Gamma 0 :6 a Gamma Q performs an a, then with probability 40 it will be the one on the left, and with probability 60 it will be the one on the right. ....

....the probability that P performs a trace from A given that the environment is willing to perform the trace y (and nothing else) This allows her to give a semantics to external choice, but unfortunately, it is not possible to give a semantic definition for hiding in this way. In my thesis [Low93b] I gave a semantic model that covered both internal and external probabilistic behaviour in a probabilistic version of Timed CSP. However, as described above, it was necessary to consider prioritized behaviour, and this resulted in a very complicated semantic model. A common theme between these ....

Gavin Lowe. Probabilities and Priorities in Timed CSP. D. Phil thesis, Oxford, 1993.

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G. Lowe. Probabilities and Priorities in Timed CSP. PhD thesis, Oxford University Computing Laboratory, 1993.

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Gavin Lowe. Probabilities and Priorities in Timed CSP. PhD thesis, Universit of Oxford, 1993.

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Gavin Lowe. Probabilities and Priorities in Timed CSP. D. Phil thesis, Oxford, 1993.

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