Geodesic
Finding periods of Zhegalkin polynomials
Diskretnaya Matematika, Tome 33 (2021) no. 3, pp. 107-120

Voir la notice de l'article provenant de la source Math-Net.Ru

A period of a Boolean function $f(x_1, \ldots, x_n)$ is a binary $n$-tuple $a = (a_1, \ldots, a_n)$ that satisfies the identity $f(x_1+a_1, \ldots, x_n+a_n) = f(x_1, \ldots, x_n)$. A Boolean function is periodic if it admits a nonzero period. We propose an algorithm that takes the Zhegalkin polynomial of a Boolean function $f(x_1, \ldots, x_n)$ as the input and finds a basis of the space of all periods of $f(x_1, \ldots, x_n)$. The complexity of this algorithm is $n^{O(d)}$, where $d$ is the degree of the function $f$. As a corollary we show that a basis of the space of all periods of a Boolean function specified by the Zhegalkin polynomial of a bounded degree may be found with complexity which is polynomial in the number of variables.
Keywords: Boolean function, Zhegalkin polynomial, periodicity, linear structure, complexity. 
@article{DM_2021_33_3_a7,
     author = {S. N. Selezneva},
     title = {Finding periods of {Zhegalkin} polynomials},
     journal = {Diskretnaya Matematika},
     pages = {107--120},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_3_a7/}
}
TY  - JOUR
AU  - S. N. Selezneva
TI  - Finding periods of Zhegalkin polynomials
JO  - Diskretnaya Matematika
PY  - 2021
SP  - 107
EP  - 120
VL  - 33
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2021_33_3_a7/
LA  - ru
ID  - DM_2021_33_3_a7
ER  - 
%0 Journal Article
%A S. N. Selezneva
%T Finding periods of Zhegalkin polynomials
%J Diskretnaya Matematika
%D 2021
%P 107-120
%V 33
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2021_33_3_a7/
%G ru
%F DM_2021_33_3_a7
S. N. Selezneva. Finding periods of Zhegalkin polynomials. Diskretnaya Matematika, Tome 33 (2021) no. 3, pp. 107-120. http://geodesic.mathdoc.fr/item/DM_2021_33_3_a7/