Improving the efficiency of using multivalued logic tools

Сулейменов, И. Э.; Vitulyova, Yelizaveta S.; Kabdushev, Sherniyaz B.; Bakirov, Akhat

doi:10.1038/s41598-023-28272-1

Cited by 7 publications

(9 citation statements)

References 24 publications

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“…The change will occur when the number 𝑛 becomes 19 • 9 = 171. In this case, 2 • 9 = 1 (17) and the value of 𝑞 becomes equal to 1.…”

Section: 𝑞 ≡ (𝑝mentioning

confidence: 99%

“…Let's consider a specific example of performing a multiplication operation in the encoding used. The product of two numbers 𝑎 1 𝑎 2 𝑎 3 and 𝑏 1 𝑏 2 𝑏 3 in the representation (17), in accordance with the above, is calculated as follows…”

Section: Number Systems With a Hybrid Base As The Basis Of The Partia...mentioning

confidence: 99%

“…Further, the theory of Galois fields is most closely related to multivalued logic [16,17]. Specifically, it is possible to match the variables of 𝑝 -valued logic, where 𝑝 is a prime number, with the elements of the Galois field 𝐺𝐹(𝑝).…”

Section: Introductionmentioning

confidence: 99%

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Convolutional neural networks from the perspective of the problems of multivalued logic

Vitulyova,

Matrassulova,

SULEIMENOV

et al. 2023

Preprint

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It is shown that it is possible to reduce the operations performed by convolutional neural networks to algebraic, and then to operations of multivalued logic. The tool for this is signal models, which are functions that take values in Galois fields and algebraic rings. This approach, among other things, allows us to switch to the use of partial convolutions, which significantly simplify the analysis of digital signals and images. Such convolutions are performed directly in terms of Galois fields, which makes it possible to use a digital analogue of the classical convolution theorem. The advantage in this regard is the possibility of using a digital analogue of transfer functions, because in terms of Fourier-Galois spectra, the convolution operation is reduced to the multiplication operation by the transfer function. This, in turn, allows us to exhaustively describe a convolutional neural network through a set of transfer functions that take values in Galois fields. The close connection between Galois fields and multivalued logics makes it possible to describe the functioning of convolutional neural networks using variables of multivalued logic.

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“…The change will occur when the number 𝑛 becomes 19 • 9 = 171. In this case, 2 • 9 = 1 (17) and the value of 𝑞 becomes equal to 1.…”

Section: 𝑞 ≡ (𝑝mentioning

confidence: 99%

Section: Number Systems With a Hybrid Base As The Basis Of The Partia...mentioning

confidence: 99%

See 1 more Smart Citation

Convolutional neural networks from the perspective of the problems of multivalued logic

Vitulyova,

Matrassulova,

SULEIMENOV

et al. 2023

Preprint

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“…In this paper, we show that the approach proposed in 20 can be generalized to the case when the number of values of multivalued logic variables is equal to .…”

Section: Introductionmentioning

confidence: 99%

“…This makes even more relevant the question of how logics of various types are related to each other, as well as the question of whether one or another of them can be reduced to others. This issue is far from being completely resolved 19 , but there is no doubt that the reduction of multivalued logics to algebraic form 20 can become an important tool for solving it.…”

Section: Introductionmentioning

confidence: 99%

Improving the efficiency of using multivalued logic tools: application of algebraic rings

Suleimenov,

Vitulyova,

Kabdushev

et al. 2023

Sci Rep

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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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