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University proceedings. Volga region. Physical and mathematical sciences, 2010, Issue 1, Pages 64–79
(Mi ivpnz615)
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This article is cited in 5 scientific papers (total in 5 papers)
Mathematics
On the bases in which asymptotically optimal schemes function with unreliability
A. V. Vasin Penza State University, Penza
Abstract:
We consider realization of Boolean functions by circuits composed of unreliable functional elements in some complete finite basis $B \subseteq B_3$ ($B_3$ is the set of all Boolean functions of three variables $x_1, x_2, x_3$). We assume that all elements are subjected independently of each other to inverse failures at the output with the probability $\epsilon$ ($\epsilon \in (0,1/2)$). In this article we found bases, in which almost all boolean functions is possible to realize by asymptotically optimal on reliability circuits with unreliability equal $5\epsilon$ with $\epsilon \rightarrow 0$. We proved that there are not other bases where it's possible to realize almost all boolean functions by asymptotically optimal on reliability circuits with unreliability $5\epsilon$.
Keywords:
unreliable functional elements, circuits asymptotically optimal with respect to reliability, inverse failures on outputs of elements, synthesis of circuits composed of unreliable elements.
Citation:
A. V. Vasin, “On the bases in which asymptotically optimal schemes function with unreliability”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 1, 64–79
Linking options:
https://www.mathnet.ru/eng/ivpnz615 https://www.mathnet.ru/eng/ivpnz/y2010/i1/p64
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Abstract page: | 46 | Full-text PDF : | 12 | References: | 24 |
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