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A Non-probabilistic Relational Model of Probabilistic Kleene Algebras

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Relations and Kleene Algebra in Computer Science (RelMiCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4988))

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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.

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Author information

Authors and Affiliations

  1. Faculty of Science, Kagoshima University,  

    Hitoshi Furusawa

  2. Graduate School of Science and Engineering, Kagoshima University,  

    Norihiro Tsumagari

  3. Graduate School of Information Sciences, Tohoku University,  

    Koki Nishizawa

Authors
  1. Hitoshi Furusawa
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  2. Norihiro Tsumagari
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  3. Koki Nishizawa
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Rudolf Berghammer Bernhard Möller Georg Struth

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Furusawa, H., Tsumagari, N., Nishizawa, K. (2008). A Non-probabilistic Relational Model of Probabilistic Kleene Algebras. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_10

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  • DOI: https://doi.org/10.1007/978-3-540-78913-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

  • Online ISBN: 978-3-540-78913-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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