Frequency Characteristics of Cycles in Output Sequences Generated by Combining Generators Over the Field of Two Elements

Bilyak, I. B.; Камловский, Олег Витальевич

doi:10.17223/20710410/29/2

Cited by 3 publications

(5 citation statements)

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“…In the general case (for arbitrary f ), the corresponding formula was obtained by Mezhennaya and Mikhailov [6,7]. Bilyak and Kamlovskii [1,2] got a similar result for the output sequence of the combining generator.…”

Section: Introductionmentioning

confidence: 68%

“…For it, we have W f 1 (1 (1,2) ) = 4 and W f 1 (z 1 , z 2 ) = 0 as (z 1 , z 2 ) = 1 (1,2) . According to the formula (3)…”

Section: Some Examplesmentioning

confidence: 99%

“…. , x r are output sequences of some random generators (see, e.g., [1,2,3]) and we consider them to be the content of shift registers, then the multicyclic sequence of the form (1) describes the output sequence of a combining generator [1,2]. A simple example of such a generator is the Pohl generator for which f (y 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…Well-known results describe (see, for example, [12]) the linear complexity of linear recurrent sequences, which can be assumed as register content. The properties of binary-exponent alternating sums [13] are required to study the probabilistic characteristics of sequence (1). The problem of the frequency characteristics of linear recurrent sequences, random number generators, and, in particular, sequences constructed according to rule (1), turned out to be less studied.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Number of 1's Per Cycle of a Binary Random Multicyclic Sequence

Mezhennaya¹,

Mikhailov²

2019

Int. J. of Appl. Math.

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Section: Introductionmentioning

confidence: 68%

“…For it, we have W f 1 (1 (1,2) ) = 4 and W f 1 (z 1 , z 2 ) = 0 as (z 1 , z 2 ) = 1 (1,2) . According to the formula (3)…”

Section: Some Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Number of 1's Per Cycle of a Binary Random Multicyclic Sequence

Mezhennaya¹,

Mikhailov²

2019

Int. J. of Appl. Math.

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“…Формула для частот знаков в выходной последовательности комбинирующего генератора (см. [7]), аналогичная (5), получена в [8] (см. также [9]).…”

Section: формулы для числа единицunclassified

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

Mezhennaya¹,

Mikhailov²

2019

Sib. Elektron. Mat. Izv.

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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.

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On the number of ones in outcome sequence of extended Pohl generator

Mezhennaya

Mikhailov

2020

Discrete Mathematics and Applications

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Formulas for distributions of number of ones (non-zeroes) in the cycle of the output sequence of generalized binary Pohl generator are obtained. Limit theorems for these distributions are derived in the case when the lengths of registers are coprime and tend to infinity, the contents of different registers are independent, but cell contents within each register may be dependent. The consequences of these theorems are given for the case when the contents of cells are independent random variables having equiprobable distribution on {0, 1}.

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Frequency Characteristics of Cycles in Output Sequences Generated by Combining Generators Over the Field of Two Elements

Cited by 3 publications

References 0 publications

On the Number of 1's Per Cycle of a Binary Random Multicyclic Sequence

On the Number of 1's Per Cycle of a Binary Random Multicyclic Sequence

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

On the number of ones in outcome sequence of extended Pohl generator

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