On irreduceability of Boolean functions with respect to commutative associative operation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 51-53
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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.
@article{VMUMM_2020_4_a6,
author = {G. V. Safonov and G. V. Bokov and V. B. Kudryavtsev},
title = {On irreduceability of {Boolean} functions with respect to commutative associative operation},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {51--53},
publisher = {mathdoc},
number = {4},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a6/}
}
TY - JOUR AU - G. V. Safonov AU - G. V. Bokov AU - V. B. Kudryavtsev TI - On irreduceability of Boolean functions with respect to commutative associative operation JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2020 SP - 51 EP - 53 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a6/ LA - ru ID - VMUMM_2020_4_a6 ER -
%0 Journal Article %A G. V. Safonov %A G. V. Bokov %A V. B. Kudryavtsev %T On irreduceability of Boolean functions with respect to commutative associative operation %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2020 %P 51-53 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a6/ %G ru %F VMUMM_2020_4_a6
G. V. Safonov; G. V. Bokov; V. B. Kudryavtsev. On irreduceability of Boolean functions with respect to commutative associative operation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 51-53. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a6/