Geodesic
On the complexity of monotone circuits for threshold symmetric Boolean functions
Diskretnaya Matematika, Tome 32 (2020) no. 1, pp. 81-109

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

The complexity of implementation of a threshold symmetric $n$-place Boolean function with threshold $k = O(1)$ via circuits over the basis $\{\vee,\, \wedge\}$ is shown not to exceed $2 \log_2 k \cdot n + o(n)$. Moreover, the complexity of a threshold-2 function is proved to be $2n+\Theta(\sqrt n)$, and the complexity of a threshold-3 function is shown to be $3n+O(\log n) $, the corresponding lower bounds are put forward.
Keywords: monotone circuits, complexity, symmetric Boolean functions, threshold functions. 
@article{DM_2020_32_1_a6,
     author = {I. S. Sergeev},
     title = {On the complexity of monotone circuits for threshold symmetric {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {81--109},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_1_a6/}
}
TY  - JOUR
AU  - I. S. Sergeev
TI  - On the complexity of monotone circuits for threshold symmetric Boolean functions
JO  - Diskretnaya Matematika
PY  - 2020
SP  - 81
EP  - 109
VL  - 32
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2020_32_1_a6/
LA  - ru
ID  - DM_2020_32_1_a6
ER  - 
%0 Journal Article
%A I. S. Sergeev
%T On the complexity of monotone circuits for threshold symmetric Boolean functions
%J Diskretnaya Matematika
%D 2020
%P 81-109
%V 32
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2020_32_1_a6/
%G ru
%F DM_2020_32_1_a6
I. S. Sergeev. On the complexity of monotone circuits for threshold symmetric Boolean functions. Diskretnaya Matematika, Tome 32 (2020) no. 1, pp. 81-109. http://geodesic.mathdoc.fr/item/DM_2020_32_1_a6/