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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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862646566536347648 |
|---|---|
| author | Masol, V. Slobodyan, S. |
| author_facet | Masol, V. Slobodyan, S. |
| 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. |
| collection | DSpace DC |
| 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.
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| first_indexed | 2025-12-01T11:16:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4485 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-12-01T11:16:55Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On the asymptotic normality of the number of false solutions of a system of nonlinear random Boolean equations Masol, V. Slobodyan, S. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4485 |
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