Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 24-31
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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/
@article{DM_1997_9_4_a2,
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},
year = {1997},
volume = {9},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a2/}
}
TY - JOUR
AU - S. N. Selezneva
TI - On the complexity of recognizing the completeness of sets of Boolean functions realized by Zhegalkin polynomials
JO - Diskretnaya Matematika
PY - 1997
SP - 24
EP - 31
VL - 9
IS - 4
UR - http://geodesic.mathdoc.fr/item/DM_1997_9_4_a2/
LA - ru
ID - DM_1997_9_4_a2
ER -
%0 Journal Article
%A S. N. Selezneva
%T On the complexity of recognizing the completeness of sets of Boolean functions realized by Zhegalkin polynomials
%J Diskretnaya Matematika
%D 1997
%P 24-31
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/DM_1997_9_4_a2/
%G ru
%F DM_1997_9_4_a2
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.
