Abstract
We prove two theorems on the Poisson limit distribution of the number of solutions of an a priori consistent system of nonlinear random Boolean equations with stochastically independent coefficients. In particular, we assume that this system contains a linear part.
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I. N. Kovalenko and A. A. Levitskaya, “Probability properties of systems of random linear equations over finite algebraic structures,” Kibernetika, No. 3, 100–105 (1993).
G. V. Balakin, “Graphs of systems of two-term equations with Boolean variables,” Teor. Ver. Primen., 40, Issue 2, 241–259 (1995).
V. A. Kopyttsev, “On the distribution of the number of solutions of random a priori consistent systems of equations,” Teor. Ver. Primen., 40, Issue 2, 430–437 (1995).
V. I. Masol, “Poisson theorems for the limit distribution of the number of solutions of a system of nonlinear random Boolean equations,” in: Abstracts of the Second All-Russian School on Stochastic Methods [in Russian], TVP, Moscow (1995), pp. 95–96.
G. E. Andrews, Theory of Partitions [Russian translation], Nauka, Moscow (1982).
V. I. Masol, “Moments of the number of solutions of a system of random Boolean equations,” in: Random Operators and Stochastic Equations, 1, No. 2, 171–179 (1993).
V. N. Sachkov, Introduction to Combinatorial Methods of Discrete Mathematics [in Russian], Nauka, Moscow (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1214–1226, September, 1998.
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Masol, V.I. Limit distribution of the number of solutions of a system of random Boolean equations with a linear part. Ukr Math J 50, 1389–1404 (1998). https://doi.org/10.1007/BF02525245
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DOI: https://doi.org/10.1007/BF02525245