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. © 2008 Springer-Verlag Berlin Heidelberg.
Cite
CITATION STYLE
Furusawa, H., Tsumagari, N., & Nishizawa, K. (2008). A non-probabilistic relational model of probabilistic kleene algebras. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4988 LNCS, pp. 110–122). Springer Verlag. https://doi.org/10.1007/978-3-540-78913-0_10
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