Tracing Relations Probabilistically

Article type: Research Article

Authors: Doberkat, Ernst-Erich

Affiliations: Chair for Software Technology, University of Dortmund, D-44221 Dortmund, Germany. doberkat@acm.org

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 follows 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 (nondeterministic, stochastic), representation theory

Journal: Fundamenta Informaticae, vol. 65, no. 3, pp. 193-209, 2005