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

P.R. d' Argenio, J.-P. Katoen, E. Brinksma

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    Abstract

    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 ♤) adequate to specify and analyse those systems. In order to give semantics to ♤, 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 ♤ 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 ♤ 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.
    Original languageEnglish
    Title of host publicationProgramming Concepts and Methods PROCOMET ’98
    Subtitle of host publicationIFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA
    EditorsDavid Gries, Willem-Paul de Roever
    PublisherChapman & Hall
    Chapter12
    Pages126-147
    Number of pages22
    ISBN (Electronic)978-0-387-35358-6
    ISBN (Print)0-412-83750-9
    Publication statusPublished - Jun 1998
    EventIFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998 - Shelter Island, United States
    Duration: 8 Jun 199812 Jun 1998

    Conference

    ConferenceIFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998
    Abbreviated titlePROCOMET
    CountryUnited States
    CityShelter Island
    Period8/06/9812/06/98

    Keywords

    • FMT-PA: PROCESS ALGEBRAS
    • FMT-FMPA: FORMAL METHODS FOR PERFORMANCE ANALYSIS
    • Stochastic process algebras
    • Stochastic automata
    • Probabilistic transition systems
    • Probabilistic bisimulations
    • Real-time systems

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