Geodesic
On the complexity of recognizing the completeness of sets of Boolean functions realized by Zhegalkin polynomials
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 24-31

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The existence of an algorithm with polynomial time complexity which determines whether a system of Boolean functions realized in the form of Zhegalkin polynomial is complete is proved. It is also proved that if $l$ is the length and $r$ is the rank of the polynomial for a Boolean function, then $l\ge\sqrt{2^r}-1$ for a self-dual function and $l\ge\sqrt{2^r}$ for an even function. 
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     author = {S. N. Selezneva},
     title = {On the complexity of recognizing the completeness of sets of {Boolean} functions realized by {Zhegalkin} polynomials},
     journal = {Diskretnaya Matematika},
     pages = {24--31},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a2/}
}
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S. N. Selezneva. On the complexity of recognizing the completeness of sets of Boolean functions realized by Zhegalkin polynomials. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 24-31. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a2/