Abstraction in Probabilistic Process Algebra

  • S. Andova
  • J. C. M. Baeten
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2031)


Process algebras with abstraction have been widely used for the specification and verification of non-probabilistic concurrent systems. The main strategy in these algebras is introducing a constant, denoting an internal action, and a set of fairness rules. Following the same approach, in this paper we propose a fully probabilistic process algebra with abstraction which contains a set of verification rules as counterparts of the fairness rules in standard ACP-like process algebras with abstraction. Having probabilities present and employing the results from Markov chain analysis, these rules are expressible in a very intuitive way. In addition to this algebraic approach, we introduce a new version of probabilistic branching bisimulation for the alternating model of probabilistic systems. Different from other approaches, this bisimulation relation requires the same probability measure only for specific related processes called entries.We claim this definition corresponds better with intuition. Moreover, the fairness rules are sound in the model based on this bisimulation. Finally, we present an algorithm to decide our branching bisimulation with a polynomial-time complexity in the number of the states of the probabilistic graph.


Equivalence Class Internal Action Parallel Composition Process Algebra Probabilistic Graph 
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  1. 1.
    A. Aho, J. Hopcroft, J. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Company, 1974.Google Scholar
  2. 2.
    S. Andova, Process algebra with probabilistic choice (extended abstract), Proc. ARTS’99, Bamberg, Germany, J.-P. Katoen, ed., LNCS 1601, Springer-Verlag, pp. 111–129, 1999. Full version report CSR 99-12, Eindhoven University of Technology, 1999.Google Scholar
  3. 3.
    S. Andova, Process algebra with interleaving probabilistic parallel composition, Eindhoven University of Technology, CSR 99–04, 1999.Google Scholar
  4. 4.
    S. Andova, J.C.M. Baeten, Abstraction in probabilistic process algebra (extended abstract),
  5. 5.
    J.C.M. Baeten, J.A. Bergstra, J.W. Klop, On the consistency of Koomen’s fair abstraction rule, Theor. Comp. Sci. 51, pp.129–176, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    J.C.M. Baeten, J.A. Bergstra, S.A. Smolka, Axiomatizing probabilistic processes: ACP with generative probabilities, Information and Computation 121(2), pp. 234–255, Sep. 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J.C.M. Baeten, W. P. Weijland, Process algebra, Cambridge University Press, 1990.Google Scholar
  8. 8.
    C. Baier, On algorithmic verification methods for probabilistic systems, Habilitation thesis, Univ. Mannheim, 1998.Google Scholar
  9. 9.
    C. Baier, H. Hermanns, Weak bisimulation for fully probabilistic processes, Proc. CAV’97, LNCS 1254, pp. 119–130, 1997.Google Scholar
  10. 10.
    J.F. Groote, F. Vaandrager, An efficient algorithm for branching bisimulation and stuttering equivalence, Proc. ICALP’90, LNCS 443, pp. 626–638, 1990.Google Scholar
  11. 11.
    C.-C. Jou, Aspects of probabilistic process algebra, Ph.D.Thesis, State University of New York at Stony Brook, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • S. Andova
    • 1
  • J. C. M. Baeten
    • 1
  1. 1.Department of Computing ScienceEindhoven University of TechnologyThe Netherlands

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