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.
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References
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)
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)
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)
Doberkat, E.-E.: Stochastic relations interpreting modal logic. Technical Report 144, Chair for Software-Technology, University of Dortmund (October 2003)
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, Montreals
Parthasarathy, K.R.: Probability Measures on Metric Spaces. Academic Press, New York (1967)
Srivastava, S.M.: A Course on Borel Sets. Graduate Texts in Mathematics, vol. 180. Springer, Berlin (1998)
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Doberkat, EE. (2004). Tracing Relations Probabilistically. In: Berghammer, R., Möller, B., Struth, G. (eds) Relational and Kleene-Algebraic Methods in Computer Science. RelMiCS 2003. Lecture Notes in Computer Science, vol 3051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24771-5_8
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DOI: https://doi.org/10.1007/978-3-540-24771-5_8
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