On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations
The theorem on a normal limit (n → ∞) distribution of the number of false solutions of a system of nonlinear Boolean equations with independent random coefficients is proved. In particular, we assume that each equation has coefficients that take value 1 with probability that varies in some neighborh...
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| Datum: | 2007 |
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| Sprache: | English |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/4485 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations / V. Masol, S. Slobodyan // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 1-2. — С. 144-151. — Бібліогр.: 5 назв.— англ. |
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Masol, V. Slobodyan, S. 2009-11-19T10:18:19Z 2009-11-19T10:18:19Z 2007 On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations / V. Masol, S. Slobodyan // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 1-2. — С. 144-151. — Бібліогр.: 5 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4485 The theorem on a normal limit (n → ∞) distribution of the number of false solutions of a system of nonlinear Boolean equations with independent random coefficients is proved. In particular, we assume that each equation has coefficients that take value 1 with probability that varies in some neighborhood of the point 1/2; the system has a solution with the number of ones equals ρ(n), ρ(n) → ∞ as n → ∞. The proof is constructed on the check of auxiliary statement conditions which in turn generalizes one well-known result. en Інститут математики НАН України On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations |
| spellingShingle |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations Masol, V. Slobodyan, S. |
| title_short |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations |
| title_full |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations |
| title_fullStr |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations |
| title_full_unstemmed |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations |
| title_sort |
on the asymptotic normality of the number of false solutions of a system of nonlinear random boolean equations |
| author |
Masol, V. Slobodyan, S. |
| author_facet |
Masol, V. Slobodyan, S. |
| publishDate |
2007 |
| language |
English |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The theorem on a normal limit (n → ∞) distribution of the number of false solutions of a system of nonlinear Boolean equations with independent random coefficients is proved. In particular, we assume that each equation has coefficients that take value 1 with probability that varies in some neighborhood of the point 1/2; the system has a solution with the number of ones equals ρ(n), ρ(n) → ∞ as n → ∞. The proof is constructed on the check of auxiliary statement conditions which in turn generalizes one well-known result.
|
| issn |
0321-3900 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/4485 |
| citation_txt |
On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations / V. Masol, S. Slobodyan // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 1-2. — С. 144-151. — Бібліогр.: 5 назв.— англ. |
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AT masolv ontheasymptoticnormalityofthenumberoffalsesolutionsofasystemofnonlinearrandombooleanequations AT slobodyans ontheasymptoticnormalityofthenumberoffalsesolutionsofasystemofnonlinearrandombooleanequations |
| first_indexed |
2025-12-01T11:16:55Z |
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2025-12-01T11:16:55Z |
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1850860086520446976 |