### ON THE ASYMPTOTIC NORMALITY OF THE NUMBER OF FALSE SOLUTIONS OF A SYSTEM OF NONLINEAR RANDOM BOOLEAN EQUATIONS

**VOLODYMYR MASOL AND SVITLANA SLOBODYAN**

*Theory of Stochastic Processes*

*Vol.13 (29), no.1-2, 2007, pp.144-151*

The theorem on a normal limit $(n\to\infty)$ 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 $\frac{1}{2}$ the system has a solution with the number of ones equals $\rho(n)$, $\rho(n)\to \infty$ as $n\to\infty$. The proof is constructed on the check of auxiliary statement conditions which in turn generalizes one well-known result.

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