Geodesic
The complexity of the realization of symmetrical functions by formulae
Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 109-120.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@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},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {1972},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a12/
%G ru
%F MZM_1972_11_1_a12
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/