Geodesic
About basises whose unreliability coefficient equals 1
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 56-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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Circuits composed of unreliable functional elements in a complete finite basis $B$ are considered. It is assumed that all elements are independently of each other subjected to inverse failures at the outputs with the probability $\varepsilon$ ($\varepsilon \in (0, 1/2)$). In the paper, a set $G$ of Boolean functions is found, and it is proved that if $B\cap G\neq\emptyset$, then almost all Boolean functions are realized in basis $B$ by asymptotically optimal on reliability circuits with unreliability $\varepsilon$ under $\varepsilon\to 0$.
Keywords: unreliable functional gates, circuits asymptotically optimal with respect to reliability, inverse failures on outputs of gates. 
@article{PDMA_2013_6_a26,
     author = {A. V. Vasin},
     title = {About basises whose unreliability coefficient equals~1},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {56--57},
     year = {2013},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a26/}
}
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A. V. Vasin. About basises whose unreliability coefficient equals 1. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 56-57. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a26/

[1] Lupanov O. P., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, Izd-vo Mosk. un-ta, M., 1984

[2] Vasin A. V., Asimptoticheski optimalnye po nadezhnosti skhemy v polnykh bazisakh iz trekhvkhodovykh elementov, dis. ... kand. fiz.-mat. nauk, Penza, 2010, 100 pp.