Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 109-120
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V. M. Khrapchenko. The complexity of the realization of symmetrical functions by formulae. Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 109-120. http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a12/
@article{MZM_1972_11_1_a12,
author = {V. M. Khrapchenko},
title = {The complexity of the realization of symmetrical functions by formulae},
journal = {Matemati\v{c}eskie zametki},
pages = {109--120},
year = {1972},
volume = {11},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a12/}
}
TY - JOUR
AU - V. M. Khrapchenko
TI - The complexity of the realization of symmetrical functions by formulae
JO - Matematičeskie zametki
PY - 1972
SP - 109
EP - 120
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a12/
LA - ru
ID - MZM_1972_11_1_a12
ER -
%0 Journal Article
%A V. M. Khrapchenko
%T The complexity of the realization of symmetrical functions by formulae
%J Matematičeskie zametki
%D 1972
%P 109-120
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a12/
%G ru
%F MZM_1972_11_1_a12
It is proved that every symmetric function in $k$-valued logic of $n$ arguments can be realized by a formula in any basis, the complexity of the formula not exceeding $n^C$, where $C$ is a constant depending on the basis. It is shown that in the case $k=2$, $C\leqslant 4,93$ for all bases.
