A non-probabilistic relational model of probabilistic Kleene algebras

Authors:
Hitoshi Furusawa;Norihiro Tsumagari;Koki Nishizawa
Affiliations:
Faculty of Science, Kagoshima University;Graduate School of Science and Engineering, Kagoshima University;Graduate School of Information Sciences, Tohoku University
Venue:
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Year:
2008

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Abstract

This paper studies basic properties of up-closed multirelations, and then shows that the set of finitary total up-closed multirelations over a set forms a probabilistic Kleene algebra. In Kleene algebras, the star operator is very essential. We investigate the reflexive transitive closure of a finitary up-closed multirelation and show that the closure operator plays a rôle of the star operator of a probabilistic Kleene algebra consisting of the set of finitary total up-closed multirelations as in the case of a Kozen's Kleene algebra consisting of the set of (usual) binary relations.