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Tracing Relations Probabilistically

  • Ernst-Erich Doberkat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)

Abstract

We investigate similarities between non-deterministic and probabilistic ways of describing a system in terms of computation trees. We show that the construction of traces for both kinds of relations follow the same principles of construction. Representations of measurable trees in terms of probabilistic relations are given. This shows that stochastic relations may serve as refinements of their non-deterministic counterparts. A convexity argument formalizes the observation that non-deterministic system descriptions are underspecified when compared to probabilistic ones. The mathematical tools come essentially from the theory of measurable selections.

Keywords

Probabilistic relations specification techniques non-deterministic stochastic representation theory 

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References

  1. 1.
    Abramsky, S., Blute, R., Panangaden, P.: Nuclear and trace ideal in tensored *- categories. Journal of Pure and Applied Algebra 143(1– 3), 3–47 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Doberkat, E.-E.: The demonic product of probabilistic relations. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 113–127. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Doberkat, E.-E.: The converse of a probabilistic relation. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 233–249. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Doberkat, E.-E.: Stochastic relations interpreting modal logic. Technical Report 144, Chair for Software-Technology, University of Dortmund (October 2003)Google Scholar
  5. 5.
    Panangaden, P.: Probabilistic relations. In: Baier, C., Huth, M., Kwiatkowska, M., Ryan, M. (eds.) Proc. PROBMIV, pp. 59–74 (1998), Also available from the School of Computer Science, McGill University, MontrealsGoogle Scholar
  6. 6.
    Parthasarathy, K.R.: Probability Measures on Metric Spaces. Academic Press, New York (1967)zbMATHGoogle Scholar
  7. 7.
    Srivastava, S.M.: A Course on Borel Sets. Graduate Texts in Mathematics, vol. 180. Springer, Berlin (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ernst-Erich Doberkat
    • 1
  1. 1.Chair for Software TechnologyUniversity of Dortmund 

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