This article is cited in 7 papers

A theorem on the limiting distribution for the number of false solutions of a system of nonlinear random Boolean equations

V. I. Masol

National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics

Abstract: We prove that the distribution of the number of false solutions of a consistent system of nonlinear random Boolean equations with stochastically independent coefficients is asymptotically Poisson with parameter $2^m$ as the number $n$ of unknowns tends to infinity. Our principal assumptions are: the distributions of the coefficients vary in a vicinity of the point $\frac 12$, $n$ and the number $N$ of equations of the system differ by a constant $m$ as $n\to\infty$; the system has a solution which contains $\rho(n)$ units, where $\rho(n)\to\infty$ as $n\to\infty$.

Keywords: the number of false solutions, Poisson distribution, nonlinear random Boolean equations.

Received: 08.04.1996

DOI: 10.4213/tvp822

 English version: Theory of Probability and its Applications, 1999, 43:1, 75–88

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