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Diskretnyi Analiz i Issledovanie Operatsii, 2013, Volume 20, Issue 6, Pages 3–15
(Mi da749)
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Asymptotically reliability optimal schemes in special bases
A. V. Vasin Penza State University, 40 Krasnaya St., 220030 Penza, Russia
Abstract:
We consider realization of Boolean functions by circuits composed of unreliable functional elements in some complete finite basis $B\subset B_3$ ($B_3$ is the set of all Boolean functions of three variables $x_1,x_2$ and $x_3$). We assume that all elements are independently of each other subjected to inverse failures at the output with the probability $\varepsilon\in(0;1/2)$. We find bases in which it is possible to realize almost all Boolean functions by asymptotically reliability optimal circuits with unreliability $3\varepsilon$ with $\varepsilon\to0$. We proved that there are no other bases where it's possible to realize almost all Boolean functions by asymptotically reliability optimal circuits with unreliability $3\varepsilon$. Bibliogr. 9.
Keywords:
unreliable functional element, asymptotically reliability optimal circuit, inverse failure on outputs of elements, synthesis of a circuit composed of unreliable elements.
Received: 12.04.2010 Revised: 17.01.2013
Citation:
A. V. Vasin, “Asymptotically reliability optimal schemes in special bases”, Diskretn. Anal. Issled. Oper., 20:6 (2013), 3–15; J. Appl. Industr. Math., 8:1 (2014), 127–135
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https://www.mathnet.ru/eng/da749 https://www.mathnet.ru/eng/da/v20/i6/p3
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Abstract page: | 168 | Full-text PDF : | 56 | References: | 39 | First page: | 3 |
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