Geodesic
Asymptotically reliability optimal schemes in special bases
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 6, pp. 3-15

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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. 
@article{DA_2013_20_6_a0,
     author = {A. V. Vasin},
     title = {Asymptotically reliability optimal schemes in special bases},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {20},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2013_20_6_a0/}
}
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A. V. Vasin. Asymptotically reliability optimal schemes in special bases. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 6, pp. 3-15. http://geodesic.mathdoc.fr/item/DA_2013_20_6_a0/