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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 1, Pages 51–61 (Mi tvp684)

On the Limit Distribution of the Number of Solutions of a Random Linear System in the Glass of Boolean Functions

I. N. Kovalenko

Moscow

Abstract: Let (1) be a system of linear Boolean equations, $a_{ij}$ being independent random variables with distributions given by (2). Let $\nu_n$ denote the number of linearly independent solutions of the system. Condition (3) with some fixed $\delta>0$ implies the convergence of the distributions of $\nu_n$ as $n\to\infty$ to the distribution of a random variable $\nu$ which can be constructed as follows:
$$\nu= \begin{cases} 0&if\quad m+s_{k_0}\le0 m+s_{k_0}&if\quad m+s_{k_0}>0 \end{cases}$$
where die distribution of $s_{k_0}$ is given by (24), (25).

Full text: PDF file (590 kB)

English version:
Theory of Probability and its Applications, 1967, 12:1, 47–56

Bibliographic databases:

Citation: I. N. Kovalenko, “On the Limit Distribution of the Number of Solutions of a Random Linear System in the Glass of Boolean Functions”, Teor. Veroyatnost. i Primenen., 12:1 (1967), 51–61; Theory Probab. Appl., 12:1 (1967), 47–56

Citation in format AMSBIB
\Bibitem{Kov67} \by I.~N.~Kovalenko \paper On the Limit Distribution of the Number of Solutions of a~Random Linear System in the Glass of Boolean Functions \jour Teor. Veroyatnost. i Primenen. \yr 1967 \vol 12 \issue 1 \pages 51--61 \mathnet{http://mi.mathnet.ru/tvp684} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=219119} \zmath{https://zbmath.org/?q=an:0201.51002|0183.20305} \transl \jour Theory Probab. Appl. \yr 1967 \vol 12 \issue 1 \pages 47--56 \crossref{https://doi.org/10.1137/1112005}