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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Normal limiting distribution of the normalized number of extraneous solutions of a compatible system of nonlinear random equations over the field GF(2)

V. I. Masol, S. Ya. Slobodyan

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Abstract: Conditions are presented under which the distribution of the properly normalized number of extraneous solutions of a system of compatible random equations over the field GF(2) tends to a standard normal distribution.

Keywords: Random equations, field GF(2), limiting normal distribution, extraneous solutions

Bibliography:
1. V. I. Masol, Moments of the number of solutions of system of random Boolean equations, Random Oper. Stoch. Eq. 1 (1993), no. 2, 171-179.
2. V. I. Masol and S. Y. Slobodyan, On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations, Theory Stoch. Process. 13(29) (2007), no. 1-2, 144-151.
3. V. I. Masol, A theorem on the limiting distribution for the number of false solutions of a system of nonlinear random Boolean equations, Teor. Veroyatnost. Primenen. 43 (1998), no. 1, 41-56; English transl. in Theory Probab. Appl. 43 (1999), no. 1, 75-88.
4. V. G. Mikhań≠lov, Limit theorems for the number of nonzero solutions of a system of random equations over GF(2), Teor. Veroyatnost. Primenen. 43 (1998), no. 3, 598-606; English transl. in Theory Probab. Appl. 43 (1999), no. 3, 480-487.
5. K. A. Rybnikov, Introduction to Combinatorial Analysis, 2nd edition, Moscow University Press, Moscow, 1985. (Russian)