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International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications

ICTERI 2014: Information and Communication Technologies in Education, Research, and Industrial Applications pp 117–138Cite as

On Algebraic Properties of Nominative Data and Functions

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 469))

Abstract

In the chapter basic properties of nominative data and functions over nominative data (nominative functions) are investigated from the perspective of abstract algebra. A set of all nominative data over arbitrary fixed sets of names and values together with basic operations which include naming, denaming, and overlapping is considered as an algebraic structure and its main properties are studied. Nominative data with complex names satisfy the principle of associative naming and processing. For such data a natural equivalence relation is introduced. Properties of nominative functions (mathematical models of programs over nominative data) and predicates are studied. A notion of nominative stability of nominative functions and predicates is considered. A two-sorted algebra of nominative functions and predicates which generalizes Glushkov algorithmic algebras is introduced and it is proved that the set of nominative stable functions and the set of nominative stable predicates constitute its sub-algebra. The obtained results form a mathematical basis for nominative program logic construction.

This work was supported in part by the research project No. 11BF015-02 “Formal specifications and methods of development of reliable software systems”, Taras Shevchenko National University of Kyiv, Ukraine.

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Donetsk, Ukraine

    Volodymyr G. Skobelev

  2. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Mykola Nikitchenko & Ievgen Ivanov

Authors
  1. Volodymyr G. Skobelev
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  2. Mykola Nikitchenko
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  3. Ievgen Ivanov
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Corresponding author

Correspondence to Ievgen Ivanov .

Editor information

Editors and Affiliations

  1. Zaporizhzhya National University, Zaporizhzhya, Ukraine

    Vadim Ermolayev

  2. Institute of Applied Informatics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Heinrich C. Mayr

  3. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Mykola Nikitchenko

  4. Kherson State University, Kherson, Ukraine

    Aleksander Spivakovsky

  5. V.N. Karazin Kharkiv National University, Kharkov, Ukraine

    Grygoriy Zholtkevych

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Skobelev, V.G., Nikitchenko, M., Ivanov, I. (2014). On Algebraic Properties of Nominative Data and Functions. In: Ermolayev, V., Mayr, H., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2014. Communications in Computer and Information Science, vol 469. Springer, Cham. https://doi.org/10.1007/978-3-319-13206-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-13206-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13205-1

  • Online ISBN: 978-3-319-13206-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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