Geodesic
About basises whose unreliability coefficient equals 1
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 56-57

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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. 
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/
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     author = {A. V. Vasin},
     title = {About basises whose unreliability coefficient equals~1},
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[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.