Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2022, Number 3, Pages 32–40 (Mi vmumm4473)  

Mathematics

Refined bounds on Shannon’s function for complexity of circuits of functional elements

S. A. Lozhkin

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
References:
Abstract: Earlier, the author proposed rather general approaches and methods for obtaining high accuracy and close to high accuracy asymptotic bounds on Shannon's function for complexity in various classes of circuits. Most of the results obtained with their aid were published in a number of papers, except perhaps for the close to the high accuracy asymptotic bounds on Shannon's function for the complexity of circuits without restrictions on their structure. This paper fills this gap and presents a modified and simplified version of one of the above-mentioned methods, which, nevertheless, allows one to obtain bounds with the required accuracy.
Key words: Boolean function, circuits of the functional elements, complexity, high accuracy asymptotic bounds.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-15 2019-1621
Received: 10.02.2022
English version:
Moscow University Mathematics Bulletin, 2022, Volume 77, Issue 3, Pages 144–153
DOI: https://doi.org/10.3103/S002713222203007X
Bibliographic databases:
Document Type: Article
UDC: 519.95
Language: Russian
Citation: S. A. Lozhkin, “Refined bounds on Shannon’s function for complexity of circuits of functional elements”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 32–40; Moscow University Mathematics Bulletin, 77:3 (2022), 144–153
Citation in format AMSBIB
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\by S.~A.~Lozhkin
\paper Refined bounds on Shannon’s function for complexity of circuits of functional elements
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2022
\issue 3
\pages 32--40
\mathnet{http://mi.mathnet.ru/vmumm4473}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4481000}
\zmath{https://zbmath.org/?q=an:7596808}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2022
\vol 77
\issue 3
\pages 144--153
\crossref{https://doi.org/10.3103/S002713222203007X}
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