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Probabilistic Simulations for Probabilistic Processes
, 1994
"... Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed ..."
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Cited by 370 (22 self)
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Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.
Compositional Methods for Probabilistic Systems
, 2001
"... We present a compositional tracebased model for probabilistic systems. The behavior of a system with probabilistic choice is a stochastic process, namely, a probability distribution on traces, or "bundle." Consequently, the semantics of a system with both nondeterministic and probabilisti ..."
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Cited by 50 (0 self)
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We present a compositional tracebased model for probabilistic systems. The behavior of a system with probabilistic choice is a stochastic process, namely, a probability distribution on traces, or "bundle." Consequently, the semantics of a system with both nondeterministic and probabilistic choice is a set of bundles. The bundles of a composite system can be obtained by combining the bundles of the components in a simple mathematical way. Re nement between systems is bundle containment. We achieve assumeguarantee compositionality for bundle semantics by introducing two scoping mechanisms. The first mechanism, which is standard in compositional modeling, distinguishes inputs from outputs and hidden state. The second mechanism, which arises in probabilistic systems, partitions the state into probabilistically independent regions.
Probabilistic metric semantics for a simple language with recursion
 Proc. Mathematical Foundations of Computer Science (MFCS), volume 1113 of Lecture Notes in Computer Science
, 1996
"... Abstract. We consider a simple divergencefree language RP for reactive processes which includes prefixing, deterministic choice, actionguarded probabilistic choice, synchronous parallel and recursion. We show that the probabilistic bisimulation of Larsen & Skou is a congruence for this language ..."
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Cited by 19 (6 self)
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Abstract. We consider a simple divergencefree language RP for reactive processes which includes prefixing, deterministic choice, actionguarded probabilistic choice, synchronous parallel and recursion. We show that the probabilistic bisimulation of Larsen & Skou is a congruence for this language. Following the methodology introduced by de Bakker & Zucker we give denotational semantics to this language by means of a complete metric space of (deterministic) probabilistic trees defined in terms of the powerdomain of closed sets. This new metric, although not an ultrametric, nevertheless specialises to the metric of de Bakker & Zucker. Our semantic domain admits a full abstraction result with respect to probabilistic bisimulation. 1
Analysing randomized distributed algorithms
 Validation of Stochastic Systems
, 2004
"... Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, thi ..."
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Cited by 14 (2 self)
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Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, this comes at a cost: the analysis of such systems become very complex, particularly in the context of distributed computation. This arises through the interplay between probability and nondeterminism. To prove a randomized distributed algorithm correct one usually involves two levels: classical, assertionbased reasoning, and a probabilistic analysis based on a suitable probability space on computations. In this paper we describe a number of approaches which allows us to verify the correctness of randomized distributed algorithms. 1
Metric semantics for reactive probabilistic processes
, 1997
"... In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these syst ..."
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Cited by 6 (1 self)
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In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these systems. Two processes are identified with respect to this equivalence if, for all experiments, the probabilities of the respective processes passing a given experiment are equal. We next consider a probabilistic process calculus including external choice, internal choice, actionguarded probabilistic choice, synchronous parallel and recursion. We give operational semantics for this calculus be means of our generalised labelled transition systems and show that our equivalence is a congruence for this language. Following the methodology introduced by de Bakker & Zucker, we then give denotational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultrametric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif
Specification and Performance of the MPEG2 Video Encoder by Using the Stochastic Process Algebra: ROSA
, 2001
"... In this paper we present the speci cation of the MPEG2 algorithm for video encoding, by using the Stochastic Process Algebra ROSA (Reasoning On Stochastic Algebras). This process algebra is a very general framework for describing and analysing concurrent systems. Thus, we also study the tempor ..."
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Cited by 6 (1 self)
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In this paper we present the speci cation of the MPEG2 algorithm for video encoding, by using the Stochastic Process Algebra ROSA (Reasoning On Stochastic Algebras). This process algebra is a very general framework for describing and analysing concurrent systems. Thus, we also study the temporal behaviour of the algorithm, by using a performance evaluation algorithm, which is also presented in this paper.
Deciding simulations on probabilistic automata
 Automated Technology for Verification and Analysis (ATVA), volume 4762 of LNCS
, 2007
"... Abstract. Probabilistic automata are a central model for concurrent systems exhibiting random phenomena. This paper presents, in a uniform setting, ecient decision algorithms for strong simulation on probabilistic automata, but with subtly dierent results. The algorithm for strong probabilistic sim ..."
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Cited by 5 (2 self)
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Abstract. Probabilistic automata are a central model for concurrent systems exhibiting random phenomena. This paper presents, in a uniform setting, ecient decision algorithms for strong simulation on probabilistic automata, but with subtly dierent results. The algorithm for strong probabilistic simulation is shown to be of polynomial complexity via a reduction to LP problem, while the algorithm for strong simulation has complexity O(m2n). The former relation allows for convex combinations of transitions in the denition and is thus less discriminative than the latter. As a byproduct, we obtain minimisation algorithms with respect to strong simulation equivalences and { for Markov decision processes { also to strong bisimulation equivalences. When extending these algorithms to the continuoustime setting, we retain same complexities for both strong and strong probabilistic simulations. 1
Domains of View: A Foundation for Specification and Analysis
, 2000
"... We propose a platform for the specification and analysis of systems. This platform contain models, their refinement and abstraction, and a temporal logic semantics; rendering a sound framework for property validation and refutation. The platform is parametric in a domain of view, an abstraction of a ..."
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Cited by 2 (2 self)
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We propose a platform for the specification and analysis of systems. This platform contain models, their refinement and abstraction, and a temporal logic semantics; rendering a sound framework for property validation and refutation. The platform is parametric in a domain of view, an abstraction of a construction based on the Plotkin power domain. For each domain of view E, the resulting platform P[E] contains partial, incomplete systems and complete systems  the actual implementations. Complete systems correspond to the platform that has as parameter a domain D that is, as a set, isomorphic to the maximal elements of E. If one restricts P[E] to implementations, but retains the temporal logic semantics, re nement, and abstraction relations, one recovers the platform P[D]. This foundation recasts existing work on modal transition systems, presents fuzzy systems, and ponders on the nature of probabilistic platforms. For domains of view E that are determined by a linearly ordered, co...