Geodesic
On domains completely specifying Boolean functions
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 21-23 
A. V. Chashkin. On domains completely specifying Boolean functions. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 21-23. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a1/
@article{DM_1997_9_4_a1,
     author = {A. V. Chashkin},
     title = {On domains completely specifying {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {21--23},
     year = {1997},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a1/}
}
TY  - JOUR
AU  - A. V. Chashkin
TI  - On domains completely specifying Boolean functions
JO  - Diskretnaya Matematika
PY  - 1997
SP  - 21
EP  - 23
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_1997_9_4_a1/
LA  - ru
ID  - DM_1997_9_4_a1
ER  - 
%0 Journal Article
%A A. V. Chashkin
%T On domains completely specifying Boolean functions
%J Diskretnaya Matematika
%D 1997
%P 21-23
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/DM_1997_9_4_a1/
%G ru
%F DM_1997_9_4_a1

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

It is shown that for an arbitrary Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ with complexity $L(f)\le2^{n-5}/n$ there exist four domains $D_1,D_2,D_3,D_4\subseteq\{0,1\}^n$ such that $f$ is completely specified by its values on these domains. If $L(f)=o(2^n)$ for $i\in\{1,\dots,4\}$, then $D_i=o(2^n)$.