A Stochastic Causality-Based Process Algebra

Brinksma, Ed; Katoen, Joost-Pieter; Langerak, Rom; Latella, Diego

doi:10.1093/comjnl/38.7.552

Cited by 41 publications

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“…Others have faced the general case [11,13,20] but the underlying semantic object usually becomes cumbersome and infinite, which makes it intractable. An alternative solution is to drop the expansion law by moving to true concurrency models [6], but for simple recursive processes, their semantic representations are infinite.…”

Section: Introductionmentioning

confidence: 99%

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An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

D’Argenio

Katoen

Brinksma

1998

Programming Concepts and Methods PROCOMET ’98

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We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named Q) adequate to specify and analyse those systems. In order to give semantics to Q, we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and Q are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too ·coarse to serve as concrete semantic objects. Therefore, we introduce a type of probabilistic transition system that can deal with arbitrary probability spaces.In addition, we give a finite axiomatisation for Q that is sound for the several semantic notions we deal with, and complete for the finest of them. Moreover, an expansion law is straightforwardly derived.

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Section: Introductionmentioning

confidence: 99%

“…In all the other cases (including the Markovian process algebras), choice is always solved either probabilistically or by the race condition. We also mention that none of [11,20,6,5] discusses an axiomatic theory for their respective stochastic process algebras.…”

mentioning

confidence: 99%

An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

D’Argenio

Katoen

Brinksma

1998

Programming Concepts and Methods PROCOMET ’98

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“…The literature presents some extensions to enrich process algebras with quantitative information such as time [52] and probabilities [67,31,42]. A further step is made by stochastic process algebras [30,36,5,11,56,9,32,18,35] which associate probabilistic distributions with prefixes. These become pairs of the form (a, F ), with the intuition that a is performed and completed in a time drawn from the distribution F .…”

Section: Process Algebras and Quantitative Measuresmentioning

confidence: 99%

“…If the transient distributions at times t and t + 1 coincide, we obtain the stationary distribution of the chain, because it will no longer change. 9 A sufficient condition for a process to be such is that all the agent identifiers occurring in it have a restricted form of definition A(Ũ ) = P . Namely, A can occur in P only if prefixed by some action and cannot occur within a parallel context.…”

Section: Stochastic Semanticsmentioning

confidence: 99%

Performance evaluation of mobile processes via abstract machines

Nottegar

Priami²,

Degano³

2001

IIEEE Trans. Software Eng.

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We use a structural operational semantics which drives us in inferring quantitative measures on system evolution. The transitions of the system are labelled and we assign rates to them by only looking at these labels. The rates reflect the possibly distributed architecture on which applications run. We then map transition systems to Markov chains, and performance evaluation is carried out using standard tools. As a working example, we compare the performance of a conventional uniprocessor with a prefetch pipeline machine. We also consider two case studies from the literature involving mobile computation to show that our framework is feasible.

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“…The basic problem within a probabilistic concurrent description language is constructing the representation of parallel composition of two distributions [BKL95,Tof97]. In particular we need to know the consequence on a probability distribution of allowing a period of time to pass.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Approaches to Probability Distributions in Process Algebra

Tofts

2000

Form. Asp. Comput.

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One of the major problems in modelling with process algebras is that of state explosion. With the addition of information describing duration, models become more exposed to growth in the size of the description of their behaviour. We describe a symbolic approach to the description of duration information within a probabilistic calculus that has two benefits: firstly we can describe behaviour without instantiating distributions; secondly we can control the growth in our system representation as a trade against model accuracy. We can compute upper bounds on performance without the inclusion of additional state information in our systems. A large example, from the discrete event simulation literature, is presented to demonstrate the effectiveness of the approach.

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A Stochastic Causality-Based Process Algebra

Cited by 41 publications

References 0 publications

An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

Performance evaluation of mobile processes via abstract machines

Symbolic Approaches to Probability Distributions in Process Algebra

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