Affiliation:
1. Lomonosov Moscow State University , Moscow , Russia
Abstract
Abstract
A period of a Boolean function f(x
1, …, x
n
) is a binary n-tuple a = (a
1, …, a
n
) that satisfies the identity f(x
1 + a
1, …, xn
+ a
n
) = f(x
1, …, 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, …, x
n
) as the input and finds a basis of the space of all periods of f(x
1, …, 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.
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
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