Doklady Mathematics

, Volume 98, Issue 2, pp 421–424 | Cite as

On Correctness Conditions for Algebra of Recognition Algorithms with μ-Operators over Pattern Problems with Binary Data

  • A. E. Dyusembaev
  • M. V. Grishko


The concept of an Ω-weakly regular problem is introduced. On the basis of the Zhuravlev operator approach combined with the neural network paradigm, it is shown that, for each such problem, a correct algorithm and a six-level spatial neural network reproducing the computations executed by this algorithm can be constructed. Moreover, the set of Ω-weakly regular problems includes the set of Ω-regular problems. It turns out that a three-level spatial network (μ-block) is a forward propagation network whose inner loop under estimation of the class membership for each test object consists of a single iteration. As a result, the amount of computations required for the six-level network is reduced noticeably.


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  1. 1.
    Yu. I. Zhuravlev, Selected Papers (Magistr, Moscow, 1998) [in Russian].Google Scholar
  2. 2.
    Yu. I. Zhuravlev, Kibernetika, No. 2, 37–45 (1978).Google Scholar
  3. 3.
    A. E. Dyusembaev and M. V. Grishko, J. Pattern Recogn. Image Anal. 27 (2), 166–174 (2017).CrossRefGoogle Scholar
  4. 4.
    A. E. Dyusembaev and D. R. Kaliazhdarov, Dokl. Math. 91 (2), 236–239 (2015).MathSciNetCrossRefGoogle Scholar
  5. 5.
    A. E. Dyusembaev, Dokl. Math. 95 (2), 125–128 (2017).MathSciNetCrossRefGoogle Scholar
  6. 6.
    A. E. Dyusembaev, USSR Comput. Math. Math. Phys. 22 (6), 217–226 (1982).MathSciNetCrossRefGoogle Scholar
  7. 7.
    M. A. Solov’ev, Tests (Theory, Constructions, and Applications) (Nauka, Moscow, 1978) [in Russian].zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsAl-Farabi National University of KazakhstanAlmatyKazakhstan

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