A Testing Scenario for Probabilistic Automata

  • Mariëlle Stoelinga
  • Frits Vaandrager
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)


Recently, a large number of equivalences for probabilistic automata has been proposed in the literature. Except for the probabilistic bisimulation of Larsen & Skou, none of these equivalences has been characterized in terms of an intuitive testing scenario. In our view, this is an undesirable situation: in the end, the behavior of an automaton is what an external observer perceives. In this paper, we propose a simple and intuitive testing scenario for probabilistic automata and we prove that the equivalence induced by this scenario coincides with the trace distribution equivalence proposed by Segala.


Testing Scenario Probabilistic Choice Label Transition System Testing Relation Trace Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BBK87]
    J.C.M. Baeten, J.A. Bergstra, and J.W. Klop. On the consistency of Koomen’s fair abstraction rule. Theoretical Computer Science, 51(1/2):129–176, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [BK86]
    J.A. Bergstra and J.W. Klop. Verification of an alternating bit protocol by means of process algebra. In W. Bibel and K.P. Jantke, editors, Math. Methods of Spec. and Synthesis of Software Systems’ 85, Math. Research 31, pages 9–23, Berlin, 1986. Akademie-Verlag.Google Scholar
  3. [CDSY99]
    R. Cleaveland, Z. Dayar, S. A. Smolka, and S. Yuen. Testing preorders for probabilistic processes. Information and Computation, 154(2):93–148, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [Chr90]
    I. Christoff. Testing equivalence and fully abstract models of probabilistic processes. In J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR 90, Amsterdam, volume 458 of Lecture Notes in Computer Science. Springer-Verlag, 1990.Google Scholar
  5. [Coh80]
    D.L. Cohn. Measure Theory. Birkhäuser, Boston, 1980.zbMATHGoogle Scholar
  6. [DNH84]
    R. De Nicola and M. Hennessy. Testing equivalences for processes. Theoretical Computer Science, 34:83–133, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Gla01]
    R.J. van Glabbeek. The linear time — branching time spectrum I. The semantics of concrete, sequential processes. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra, pages 3–99. North-Holland, 2001.Google Scholar
  8. [GN98]
    C. Gregorio-Rodrígez and M. Núñez. Denotational semantics for probabilistic refusal testing. In M. Huth and M.Z. Kwiatkowska, editors, Proc. ProbMIV’98, volume 22 of Electronic Notes in Theoretical Computer Science, 1998.Google Scholar
  9. [JY01]
    B. Jonsson and W. Yi. Compositional testing preorders for probabilistic processes. Theoretical Computer Science, 2001.Google Scholar
  10. [LS91]
    K.G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94:1–28, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [Mil80]
    R. Milner. A Calculus of Communicating Systems, volume 92 of Lecture Notes in Computer Science. Springer-Verlag, 1980.zbMATHGoogle Scholar
  12. [Seg95a]
    R. Segala. Compositional trace-based semantics for probabilistic automata. In Proc. CONCUR’95, volume 962 of Lecture Notes in Computer Science, pages 234–248, 1995.Google Scholar
  13. [Seg95b]
    R. Segala. Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, June 1995. Available as Technical Report MIT/LCS/TR-676.Google Scholar
  14. [Seg96]
    R. Segala. Testing probabilistic automata. In Proc. CONCUR’96, volume 1119 of Lecture Notes in Computer Science, pages 299–314, 1996.Google Scholar
  15. [SL95]
    R. Segala and N.A. Lynch. Probabilistic simulations for probabilistic processes. Nordic Journal of Computing, 2(2):250–273, 1995.zbMATHMathSciNetGoogle Scholar
  16. [Sto02a]
    M.I.A. Stoelinga. Alea jacta est: verification of probabilistic, real-time and parametric systems. PhD thesis, University of Nijmegen, the Netherlands, April 2002. Available via Scholar
  17. [Sto02b]
    M.I.A. Stoelinga. An introduction to probabilistic automata. In G. Rozenberg, editor, EATCS bulletin, volume 78, pages 176–198, 2002.Google Scholar
  18. [SV03]
    M.I.A. Stoelinga and F.W. Vaandrager. A testing scenario for probabilistic automata. Technical Report NIII-R0307, Nijmegen Institute for Computing and Information Sciences, University of Nijmegen, 2003. Available via Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mariëlle Stoelinga
    • 1
  • Frits Vaandrager
    • 2
  1. 1.Dept. of Computer EngineeringUniversity of CaliforniaSanta Cruz
  2. 2.Nijmegen Institute for Computing and Information SciencesUniversity of NijmegenThe Netherlands

Personalised recommendations