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Expressibility in the Kleene Algebra of Partial Predicates with the Complement Composition

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Information and Communication Technologies in Education, Research, and Industrial Applications (ICTERI 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1175))

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Abstract

In the paper we investigate the expressibility of partial predicates in the Kleene algebra extended with the composition of predicate complement and give a necessary and sufficient condition of this expressibility in terms of the existence of an optimal solution of an optimization problem. We also investigate the expressibility in the first-order Kleene algebra with predicate complement. The obtained results may be useful for software verification using an extension of the Floyd-Hoare logic for partial pre- and postconditions.

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Notes

  1. 1.

    The maximum cardinality of a subset such that any two of its distinct points are at the same distance.

  2. 2.

    If one interprets partiality in terms as possibility, minimization of ||f|| may be related to the principle of minimum specificity of D. Dubois et al. from possibility theory, or other similar principles.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, Kyiv, 01601, Ukraine

    Ievgen Ivanov & Mykola Nikitchenko

Authors
  1. Ievgen Ivanov
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  2. Mykola Nikitchenko
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Correspondence to Ievgen Ivanov .

Editor information

Editors and Affiliations

  1. Zaporizhzhia National University, Zaporizhzhia, Ukraine

    Vadim Ermolayev

  2. Université Cote d’Azur, Nice, France

    Frédéric Mallet

  3. University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

    Vitaliy Yakovyna

  4. University of Klagenfurt, Klagenfurt am Wörthersee, Austria

    Heinrich C. Mayr

  5. Kherson State University, Kherson, Ukraine

    Aleksander Spivakovsky

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Ivanov, I., Nikitchenko, M. (2020). Expressibility in the Kleene Algebra of Partial Predicates with the Complement Composition. In: Ermolayev, V., Mallet, F., Yakovyna, V., Mayr, H., Spivakovsky, A. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2019. Communications in Computer and Information Science, vol 1175. Springer, Cham. https://doi.org/10.1007/978-3-030-39459-2_3

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  • DOI: https://doi.org/10.1007/978-3-030-39459-2_3

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  • Online ISBN: 978-3-030-39459-2

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