Geodesic
On the Reconstruction of a~Boolean Function from Its Values on a~Limited Number of Domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 108-122

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The problem of recovering an arbitrary Boolean function from its values on a limited number of small-sized domains is considered. For any $n$-place Boolean function $f$, it is shown that there are $\mathcal O(n)$ domains of size $\mathcal O(n\log _2n\cdot 2L(f)\log _2L(f))$ such that $f$ is uniquely determined by its values in these domains. 
@article{TM_2003_242_a8,
     author = {A. V. Chashkin},
     title = {On the {Reconstruction} of {a~Boolean} {Function} from {Its} {Values} on {a~Limited} {Number} of {Domains}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {108--122},
     publisher = {mathdoc},
     volume = {242},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2003_242_a8/}
}
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A. V. Chashkin. On the Reconstruction of a~Boolean Function from Its Values on a~Limited Number of Domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 108-122. http://geodesic.mathdoc.fr/item/TM_2003_242_a8/