On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations

Abstract

The theorem on a normal limit (n → ∞) distribution of the number of false solutions of a system of nonlinear Boolean equations with independent random coefficients is proved. In particular, we assume that each equation has coefficients that take value 1 with probability that varies in some neighborhood of the point 1/2; the system has a solution with the number of ones equals ρ(n), ρ(n) → ∞ as n → ∞. The proof is constructed on the check of auxiliary statement conditions which in turn generalizes one well-known result.