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On Algebraic Properties of Nominative Data and Functions

  • Volodymyr G. Skobelev
  • Mykola Nikitchenko
  • Ievgen Ivanov
Conference paper
Part of the Communications in Computer and Information Science book series (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.

Keywords

Glushkos algorithmic algebra Program algebra Nominative data Nominative set Named set Nominative function 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Volodymyr G. Skobelev
    • 1
  • Mykola Nikitchenko
    • 2
  • Ievgen Ivanov
    • 2
  1. 1.Institute of Applied Mathematics and Mechanics of NAS of UkraineDonetskUkraine
  2. 2.Taras Shevchenko National University of KyivKyivUkraine

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