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Reactive, Generative and Stratified Models of Probabilistic Processes
 Information and Computation
, 1990
"... ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ..."
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Cited by 155 (6 self)
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ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...
A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time
 Theoretical Computer Science
, 1998
"... In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial ..."
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Cited by 96 (9 self)
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In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial is to explain the design choices behind the development of EMPA and how the four features above interact, and to show that a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory has been achieved.
Quantifying Information Flow
 In Proc. IEEE Computer Security Foundations Workshop
, 2002
"... We extend definitions of information flow so as to quantify the amount of information passed; in other words, we give a formal definition of the capacity of covert channels. Our definition uses the process algebra CSP, and is based upon counting the number of di#erent behaviours of a high level user ..."
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Cited by 82 (1 self)
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We extend definitions of information flow so as to quantify the amount of information passed; in other words, we give a formal definition of the capacity of covert channels. Our definition uses the process algebra CSP, and is based upon counting the number of di#erent behaviours of a high level user that can be distinguished by a low level user. 1
Weak Bisimulation for Fully Probabilistic Processes
, 1999
"... Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisi ..."
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Cited by 56 (8 self)
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Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisimulation for fully probabilistic systems, transition systems where nondeterministic branching is replaced by probabilistic branching. In contrast to the nondeterministic case, both relations coincide. We give an algorithm to decide weak (and branching) bisimulation with a time complexity cubic in the number of states of the fully probabilistic system. This meets the worst case complexity for deciding branching bisimulation in the nondeterministic case. In addition, the relation is shown to be a congruence with respect to the operators of PLSCCS , a lazy synchronous probabilistic variant of CCS. We illustrate that due to these properties, weak bisimulation provides all the crucial ingredients...
Compositional Markovian modelling using a process algebra
 Numerical Solution of Markov Chains
, 1995
"... We introduce a stochastic process algebra, PEPA, as a highlevel modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model ..."
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Cited by 52 (14 self)
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We introduce a stochastic process algebra, PEPA, as a highlevel modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model. Recent extensions of these algebras, associating random variables with actions, make the models also amenable to Markovian analysis. A compositional structure is inherent in the PEPA language. As well as the clear advantages that this offers for model construction, we demonstrate how this compositionality may be exploited to reduce the state space of the CTMC. This leads to an exact aggregation based on lumpability. Moreover this technique, taking advantage of symmetries within the system, may be formally defined in terms of the PEPA description of the model. An equivalence relation, strong equivalence, developed as a process algebra bisimulation relation, is used to partition the derivation graph. 1
The Metric Analogue of Weak Bisimulation for Probabilistic Processes
, 2002
"... We observe that equivalence is not a robust concept in the presence of numerical information  such as probabilities  in the model. We develop a metric analogue of weak bisimulation in the spirit of our earlier work on metric analogues for strong bisimulation. We give a fixed point characterization ..."
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Cited by 51 (2 self)
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We observe that equivalence is not a robust concept in the presence of numerical information  such as probabilities  in the model. We develop a metric analogue of weak bisimulation in the spirit of our earlier work on metric analogues for strong bisimulation. We give a fixed point characterization of the metric. This makes available coinductive reasoning principles and allows us to prove metric analogues of the usual algebraic laws for process combinators. We also show that quantitative properties of interest are continuous with respect to the metric, which says that if two processes are close in the metric then observable quantitative properties of interest are indeed close. As an important example of this we show that nearby processes have nearby channel capacities  a quantitative measure of their propensity to leak information.
Metrics for Labelled Markov Processes
, 2003
"... The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature ..."
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Cited by 46 (10 self)
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The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Kantorovich metric.
Discounting the future in systems theory
 In Automata, Languages, and Programming, LNCS 2719
, 2003
"... ..."
The nature of synchronisation
 Proceedings of the Second International Workshop on Process Algebras and Performance Modelling
, 1994
"... In each of the current stochastic process algebras all noncompetitive interactions between components or agents are modelled using a single combinator, variously called the parallel, synchronisation or cooperation operator. This paper aims to compare the definitions of this combinator which have be ..."
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Cited by 43 (14 self)
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In each of the current stochastic process algebras all noncompetitive interactions between components or agents are modelled using a single combinator, variously called the parallel, synchronisation or cooperation operator. This paper aims to compare the definitions of this combinator which have been used; in particular, looking at the different ways in which rates are associated with the actions which result from such interactions. The implications of the chosen definitions, from a modelling point of view, will be described. When we consider concrete systems rather than abstract representations many different types of interactions between systems are exhibited. Some of these possible interactions are presented in the latter half of the paper and we analyse the extent to which these can be captured using the combinators available in the SPA languages. To conclude some observations about current modelling practice are made together with suggestions of potential extensions to the set of combinators. 1
Metrics for Labelled Markov Systems
, 2001
"... The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of ..."
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Cited by 43 (8 self)
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The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.