This article is cited in 15 papers

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:
$$ \nu= \begin{cases} 0&\text{if}\quad m+s_{k_0}\le0 \\ m+s_{k_0}&\text{if}\quad m+s_{k_0}>0 \end{cases} $$
where die distribution of $s_{k_0}$ is given by (24), (25).

Received: 25.02.1966

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

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