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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, Number 4, Pages 51–53 (Mi vmumm4341)  

Short notes

Irreducibility of Boolean functions relative to associative operation

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

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

Full text: PDF file (117 kB)
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UDC: 510.52
Received: 11.09.2019

Citation: G. V. Safonov, G. V. Bokov, V. B. Kudryavtsev, “Irreducibility of Boolean functions relative to associative operation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 51–53

Citation in format AMSBIB
\Bibitem{SafBokKud20}
\by G.~V.~Safonov, G.~V.~Bokov, V.~B.~Kudryavtsev
\paper Irreducibility of Boolean functions relative to associative operation
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2020
\issue 4
\pages 51--53
\mathnet{http://mi.mathnet.ru/vmumm4341}


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