Geodesic
On domains completely specifying Boolean functions
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 21-23.

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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 $D_i=o(2^n)$. 
@article{DM_1997_9_4_a1,
     author = {A. V. Chashkin},
     title = {On domains completely specifying {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {21--23},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a1/}
}
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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/