Article 6417

Title of the article

ON A CIRCUIT THAT INCREASES RELIABILITY IN THE BASIS CONSISTING OF A WEBB FUNCTION, AT Pk 

Authors

Alekhina Marina Anatol'evna, Doctor of physical and mathematical sciences, professor, head of sub-department of mathematics, vice-rector for research, Penza State Technological University (1a/1 Baydukova lane/Gagarina street, Penza, Russia), alekhina@penzgtu.ru

Index UDK

519.718

DOI

10.21685/2072-3040-2017-4-6

Abstract

Background. Multivalued logic opens broad opportunities to develop various algorithms in many fields. It is successfully implied for solving multiple problems and in many technical developments. This explains the interest in the problem of increasing the efficiency of circuits in the complete finite basis consisting of k-valued functions (k ≥3). The aim of the article is to build circuits suitable for increasing reliability in the basis consisting of a Webb function at random k, as well as to obtain recurrent correlations for unreliabilities of the suggested circuits and the initial circuit.
Materials and methods. The work uses well-known methods of discrete mathematics, mathematical cybernetics and mathematical analysis. Besides, the article suggests new methods for synthesizing circuits consisting of unreliable functional gates, as well as new approaches to obtaining circuit unreliability estimates. 
Results. The author has obtained the following results for the basis consisting of a Webb function: 1. One has obtained the circuits suitable for increasing reliability of initial circuits at Pk. 2. One has obtained recurrent correlations for unreliabilities of the suggested circuits and the initial circuit.

Key words

functions of k-valued logics, unreliable functional gates, synthesis of circuits composed of unreliable gates

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References

1. Alekhina M. A. Diskretnaya matematika [Discrete mathematics]. 2012, vol. 24, no. 3, pp. 17–24.
2. Alekhina M. A., Barsukova O. Yu. Diskretnyy analiz i issledovanie operatsiy [Discrete analysis and research of operations]. 2014, vol. 21, no. 4 (118), pp. 12–24.
3. Alekhina M. A., Barsukova O. Yu. Izvestiya vysshikh uchebnykh zavedeniy. Matematika [University proceedings. Mathematics]. 2015, no. 3, pp. 15–27.
4. Alekhina M. A. Izvestiya vysshikh ucheb-nykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2016, no. 3 (39), pp. 19–30.
5. Alekhina M. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2015, no. 3 (35), pp. 3–10.

 

Дата создания: 06.02.2018 10:54
Дата обновления: 23.04.2018 09:06