Geodesic
A theorem on the limiting distribution for the number of false solutions of a~system of nonlinear random Boolean equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 41-56

Voir la notice de l'article provenant de la source Math-Net.Ru

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, nonlinear random Boolean equations.
Mots-clés : Poisson distribution 
@article{TVP_1998_43_1_a2,
     author = {V. I. Masol},
     title = {A theorem on the limiting distribution for the number of false solutions of a~system of nonlinear random {Boolean} equations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {41--56},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a2/}
}
TY  - JOUR
AU  - V. I. Masol
TI  - A theorem on the limiting distribution for the number of false solutions of a~system of nonlinear random Boolean equations
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1998
SP  - 41
EP  - 56
VL  - 43
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a2/
LA  - ru
ID  - TVP_1998_43_1_a2
ER  - 
%0 Journal Article
%A V. I. Masol
%T A theorem on the limiting distribution for the number of false solutions of a~system of nonlinear random Boolean equations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1998
%P 41-56
%V 43
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a2/
%G ru
%F TVP_1998_43_1_a2
V. I. Masol. A theorem on the limiting distribution for the number of false solutions of a~system of nonlinear random Boolean equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 41-56. http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a2/