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.
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