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A Calculus of Stochastic Systems for the specification, simulation, and hidden state estimation of hybrid stochastic/non-stochastic systems

  • Albert Benveniste
  • Bernard C. Levy
  • Eric Fabre
  • Paul Le Guernic
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 999)

Abstract

In this paper, we consider mixed systems containing both stochastic and non-stochastic3 components. To compose such systems, we introduce a general combinator which allows the specification of an arbitrary mixed system in terms of elementary components of only two types. Thus, systems are obtained hierarchically, by composing subsystems, where each subsystem can be viewed as an “increment” in the decomposition of the full system. The resulting mixed stochastic system specifications are generally not “executable”, since they do not necessarily permit the incremental simulation of the system variables. Such a simulation requires compiling the dependencyrelations existing between the system variables. Another issue involves finding the most likely internal states of a stochastic system from a set of observations. We provide a small set of primitives for transforming mixed systems, which allows the solution of the two problems of incremental simulation and estimation of stochastic systems within a common framework. The complete model is called CSS (a Calculus of Stochastic Systems), and is implemented by the Sig language, derived from the Signal synchronous language. Our results are applicable to pattern recognition problems formulated in terms of Markov random fields or hidden Markov models (HMMs), and to the automatic generation of diagnostic systems for industrial plants starting from their risk analysis. A full version of this paper will appear in Theoretical Computer Science, and is available [1].

Keywords

stochastic systems mixed systems belief functions communicating processes simulation estimation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Albert Benveniste
    • 1
  • Bernard C. Levy
    • 2
  • Eric Fabre
    • 1
  • Paul Le Guernic
    • 1
  1. 1.IRISA-INRIA, Campus Universitaire de BeaulieuRennes CedexFrance
  2. 2.Dept. of of Electrical and Computer EngineeringUniv. of CaliforniaDavisUSA

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