Improving the efficiency of using multivalued logic tools: application of algebraic rings
Suleimenov I.E. Vitulyova Y.S. Kabdushev S.B. Bakirov A.S.
December 2023Nature Research
Scientific Reports
2023#13Issue 1
It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics and algebraic operations. For multivalued logics, the number of variables in which is equal to a prime number, such a connection is naturally established through explicit algebraic expressions in Galois fields. It is possible to define an algebraic δ-function, which allows you to reduce any truth table to an algebraic expression, for the case when the number of values accepted by a multivalued logic variable is equal to an integer power of a prime number. In this paper, we show that the algebraic δ-function can also be defined for the case when the number of values taken by a multivalued logic variable is p − 1, where p is a prime number. This function also allows to reduce logical operations to algebraic expressions. Specific examples of the constructiveness of the proposed approach are presented, as well as electronic circuits that experimentally prove its adequacy.
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National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, Almaty, 050010, Kazakhstan
Gumarbek Daukeyev Almaty University of Power Engineering and Telecommunications, Baytursynov Str. 126/1, Almaty, 050013, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
National Engineering Academy of the Republic of Kazakhstan
Gumarbek Daukeyev Almaty University of Power Engineering and Telecommunications
Al-Farabi Kazakh National University
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