Geodesic
On the number of significant variables of balanced Boolean function with the fixed number of elementary conjunctions in its DNF
Matematičeskie voprosy kriptografii, Tome 2 (2011), pp. 37-47

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The upper and lower bounds for the number $n(k)$ of significant variables of balanced Boolean function represented by $k$ elementary conjunction are obtained. The boundedness of $n(k)$ for every $k$ was proved by the author previously. Balanced Boolean functions are very important for cryptography; their DNF representations correspond to realizations by circuits, in particular, by programmable logical matrices. 
@article{MVK_2011_2_a2,
     author = {V. G. Nikonov},
     title = {On the number of significant variables of balanced {Boolean} function with the fixed number of elementary conjunctions in its {DNF}},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {37--47},
     publisher = {mathdoc},
     volume = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2011_2_a2/}
}
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V. G. Nikonov. On the number of significant variables of balanced Boolean function with the fixed number of elementary conjunctions in its DNF. Matematičeskie voprosy kriptografii, Tome 2 (2011), pp. 37-47. http://geodesic.mathdoc.fr/item/MVK_2011_2_a2/