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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 229–235 (Mi semr1055)

Discrete mathematics and mathematical cybernetics

On the number of ones in the cycle of multicycliñ sequence determined by Boolean function

N. M. Mezhennayaa, V. G. Mikhailovb

a Bauman Moscow State Technical University, 5, 2-aya Baumanskaya st., Moscow, 105005, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, 8, Gubkina st., Moscow, 119991, Russia

Abstract: The paper presents formulas that denote the relationship between the number of ones in the cycle of a multicyclic sequence modulo 2, defined by the Boolean function, and the number of ones in the registers of the generator through the spectral characteristics of this function. Using these formulas, we prove normal-type limit theorems for the number of ones in the cycle of the multicyclic sequence if the registers are filled with independent binary random variables with the same distributions within each register, the lengths of the registers tend to infinity and their number remains fixed. We prove that the limit distribution can be both the usual normal distribution and the distribution of the product of independent standard normal random variables.

Keywords: number of ones, multicyclic sequence, Boolean function, central limit theorem.

DOI: https://doi.org/10.33048/semi.2019.16.014

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Bibliographic databases:

Document Type: Article
UDC: 519.213, 519.214
MSC: 60F05, 94B12, 14G50
Received July 4, 2018, published February 21, 2019

Citation: N. M. Mezhennaya, V. G. Mikhailov, “On the number of ones in the cycle of multicycliñ sequence determined by Boolean function”, Sib. Èlektron. Mat. Izv., 16 (2019), 229–235

Citation in format AMSBIB
\Bibitem{MezMik19} \by N.~M.~Mezhennaya, V.~G.~Mikhailov \paper On the number of ones in the cycle of multicycliñ sequence determined by Boolean function \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 229--235 \mathnet{http://mi.mathnet.ru/semr1055} \crossref{https://doi.org/10.33048/semi.2019.16.014} `