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
Journal:
Theor. Probability and Math. Statist. 77 (2008), 121-134
MSC (2000):
Primary 60C05, 15A52, 15A03
DOI:
https://doi.org/10.1090/S0094-9000-09-00751-0
Published electronically:
January 16, 2009
MathSciNet review:
2432776
Full-text PDF Free Access
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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
- 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, DOI https://doi.org/10.1137/S0040585X97976672
- William Feller, An introduction to probability theory and its applications. Vol. I, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
- V. N. Sachkov, Vvedenie v kombinatornye metody diskretnoĭ matematiki, “Nauka”, Moscow, 1982 (Russian). MR 700691
References
- 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; English transl. in Theory Probab. Appl. 43 (1999), no. 1, 75–88. MR 1669972 (2000f:60040)
- W. Feller, An Introduction to Probability Theory and its Applications, 3rd ed., vol. I, John Wiley & Sons, New York–London–Sydney, 1968. MR 0228020 (37:3604)
- V. N. Sachkov, Introduction to Combinatorial Methods of Discrete Mathematics, “Nauka”, Moscow, 1982. (Russian) MR 700691 (85g:05001)
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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
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
