Finding periods of Zhegalkin polynomials

IF 0.3 Q4 MATHEMATICS, APPLIED
S. Selezneva
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引用次数: 0

Abstract

Abstract A period of a Boolean function f(x1, …, xn) is a binary n-tuple a = (a1, …, an) that satisfies the identity f(x1 + a1, …, xn + an) = f(x1, …, xn). 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(x1, …, xn) as the input and finds a basis of the space of all periods of f(x1, …, xn). The complexity of this algorithm is nO(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.
Zhegalkin多项式的求周期
摘要布尔函数f(x1,…,xn)的周期是二进制n元组A=(a1,…,an),它满足恒等式f(x1+a1,…,xn+an)=f(x1,…,xn)。如果布尔函数允许一个非零周期,那么它就是周期函数。我们提出了一种算法,该算法以布尔函数f(x1,…,xn)的Zhegalkin多项式为输入,并找到f(x1、…、xn)所有周期的空间的基。该算法的复杂度为nO(d),其中d是函数f的次数。作为推论,我们证明了由有界次数的Zhegalkin多项式指定的布尔函数的所有周期的空间的基可以被找到,其复杂度是变量数量的多项式。
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来源期刊
CiteScore
0.60
自引率
20.00%
发文量
29
期刊介绍: The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.
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