A theory of Stochastic systems. Part II: Process algebra

  • Authors:

  • Pedro R. D'Argenio;Joost-Pieter Katoen

  • Affiliations:

  • Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina and University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and RWTH Aachen, Ahornstraíe 55, D-52074 Aachen, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2005

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Abstract

This paper introduces (pronounce spades), a stochastic process algebra for discrete event systems, that extends traditional process algebra with timed actions whose delay is governed by general (a.o. continuous) probability distributions. The operational semantics is defined in terms of stochastic automata, a model that uses clocks-like in timed automata-to symbolically represent randomly timed systems, cf. the accompanying paper [P.R. D'Argenio, J.-P. Kateon, A theory of stochastic systems. Part I: Stochastic automata. Inf. Comput. (2005), to appear]. We show that stochastic automata and are equally expressive, and prove that the operational semantics of a term up to @a-conversion of clocks, is unique (modulo symbolic bisimulation). (Open) probabilistic and structural bisimulation are proven to be congruences for, and are equipped with an equational theory. The equational theory is shown to be complete for structural bisimulation and allows to derive an expansion law.