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Validation of Stochastic Systems pp 1–43Cite as

Probabilistic Automata: System Types, Parallel Composition and Comparison

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Abstract

We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discrete probabilities only. The expressiveness order used to built the hierarchy is defined via the existence of mappings between the corresponding system types that preserve and reflect bisimilarity. Additionally, we discuss parallel composition for the presented types of systems, augmenting the map of probabilistic automata with closedness under this compositional operator.

Keywords

  • probabilistic automata (transition systems)
  • probabilistic bisimulation
  • preservation and reflection of bisimulation
  • non-determinism
  • parallel composition

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, TU/e, Eindhoven

    Ana Sokolova

  2. LIACS, Leiden University,  

    Erik P. de Vink

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  1. Ana Sokolova
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Editors and Affiliations

  1. Institute for Theoretical Computer Science, Technical University Dresden, Germany

    Christel Baier

  2. Centre for Telematics and Information Technology, Faculty for Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500, AE, Netherlands

    Boudewijn R. Haverkort

  3. VASY, INRIA, Grenoble Rhône-Alpes, France

    Holger Hermanns

  4. Software Modeling and Verification, RWTH Aachen University, Germany

    Joost-Pieter Katoen

  5. Institut für Technische Informatik, Universität der Bundeswehr München,  

    Markus Siegle

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Sokolova, A., de Vink, E.P. (2004). Probabilistic Automata: System Types, Parallel Composition and Comparison. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, JP., Siegle, M. (eds) Validation of Stochastic Systems. Lecture Notes in Computer Science, vol 2925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24611-4_1

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