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Theory of Probability and Mathematical Statistics

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An estimate for the rate of convergence of the distribution of the number of false solutions of a system of nonlinear random equations in the field $ GF(2)$


Authors: V. I. Masol and M. V. Slobodyan
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal: Theor. Probability and Math. Statist. 77 (2008), 121-134
MSC (2000): Primary 60C05, 15A52, 15A03
Published electronically: January 16, 2009
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a result on the rate of convergence as $ n\to\infty$ of the distribution of the number of false solutions of a system of nonlinear random equations in the field $ GF(2)$ to the Poisson distribution with parameter $ 2^{m}$. We assume, in particular, that the difference between the number $ n$ of unknowns and the number $ N$ of equations of the system is a constant $ m$.


References [Enhancements On Off] (What's this?)

  • 1. V. I. Masol, A theorem on the limit distribution of the number of false solutions of a system of nonlinear random Boolean equations, Teor. Veroyatnost. i Primenen. 43 (1998), no. 1, 41–56 (Russian, with Russian summary); English transl., Theory Probab. Appl. 43 (1999), no. 1, 75–88. MR 1669972, 10.1137/S0040585X97976672
  • 2. William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
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Additional Information

V. I. Masol
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: vimasol@ukr.net

M. V. Slobodyan
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: mslob@ukr.net

DOI: https://doi.org/10.1090/S0094-9000-09-00751-0
Keywords: System of nonlinear random equations, the field $GF(2)$, rate of convergence
Received by editor(s): February 10, 2006
Published electronically: January 16, 2009
Article copyright: © Copyright 2009 American Mathematical Society