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Diskretnaya Matematika, 2022, Volume 34, Issue 4, Pages 36–51
DOI: https://doi.org/10.4213/dm1708 (Mi dm1708) 		 
On the complexity of implementation of a system of three monomials of two variables by composition circuits

S. A. Korneev

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/dm1708
Abstract: We study the complexity of implementation of systems of monomials by composition circuits. Here, by the complexity we mean the smallest possible number of operations required for computation of the system of monomials from the variables; under this approach, results of intermediate computations can be used several times. The main result of this paper establishes, for an arbitrary system of three monomials of two variables without zeroth powers, a formula for the complexity of their joint implementation by composition circuits with an additive error which is either 1 or 0.
Keywords: system of monomials, composition circuit, circuit of gates, computational complexity, circuit complexity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
Received: 15.04.2022
English version:
Discrete Mathematics and Applications, 2024, Volume 34, Issue 2, Pages 89–101
DOI: https://doi.org/10.1515/dma-2024-0008
Document Type: Article
UDC: 519.71
Language: Russian
Citation: S. A. Korneev, “On the complexity of implementation of a system of three monomials of two variables by composition circuits”, Diskr. Mat., 34:4 (2022), 36–51; Discrete Math. Appl., 34:2 (2024), 89–101
Citation in format AMSBIB
\Bibitem{Kor22}
\by S.~A.~Korneev
\paper On the complexity of implementation of a~system of three monomials of two variables by composition circuits
\jour Diskr. Mat.
\yr 2022
\vol 34
\issue 4
\pages 36--51
\mathnet{http://mi.mathnet.ru/dm1708}
\crossref{https://doi.org/10.4213/dm1708}
\transl
\jour Discrete Math. Appl.
\yr 2024
\vol 34
\issue 2
\pages 89--101
\crossref{https://doi.org/10.1515/dma-2024-0008}
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