Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2020, Number 4, Pages 51–53 (Mi vmumm4341)  
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On irreduceability of Boolean functions with respect to commutative associative operation

G. V. Safonov, G. V. Bokov, V. B. Kudryavtsev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: The paper is focused on decomposition of Boolean functions on the form $f_1\circ\ldots\circ f_m$, where $\circ$ is a commutative associative operation and $f_1,\ldots,f_m$ are Boolean functions with fewer arguments. For each commutative associative operation, we define necessary and sufficient conditions for the absence of such a decomposition and find the related complexity class.
Key words: Boolean functions, commutative associative operations, decomposition, complexity.
Received: 11.09.2019
English version:
Moscow University Mathematics Bulletin, 2020, Volume 75, Issue 4, Pages 169–171
DOI: https://doi.org/10.3103/S0027132220040051
Bibliographic databases:
Document Type: Article
UDC: 510.52
Language: Russian
Citation: G. V. Safonov, G. V. Bokov, V. B. Kudryavtsev, “On irreduceability of Boolean functions with respect to commutative associative operation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 51–53; Moscow University Mathematics Bulletin, 75:4 (2020), 169–171
Citation in format AMSBIB
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\pages 51--53
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\transl
\jour Moscow University Mathematics Bulletin
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\vol 75
\issue 4
\pages 169--171
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