Geodesic
About Circuit Reliability in Full Bases, Containing a Vote Function with Input Inverse Failures
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 2, pp. 154-163 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers Boolean functions to be realized by circuits of reliable functional elements being prone to input failures with fault probability $\varepsilon$, $0<\varepsilon<1/2,$ on any functional element input. It is shown that if to each of non-reducible full bases containing functions with at most two variables there will be added a vote function, then a reliability estimate of asymptotically optimal reliable circuits is equal $3\varepsilon^2$ (with $\varepsilon\to0$) for all Boolean functions $f(x_1,x_2,\dots,x_n)$ except for constants 0,1 and functions $x_i$, $\overline x_i$, where $i=1,\dots,n$.
Keywords: Boolean functions, asymptotically optimal reliable circuits. 
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     author = {V. V. Chugunova},
     title = {About {Circuit} {Reliability} in {Full} {Bases,} {Containing} {a~Vote} {Function} with {Input} {Inverse} {Failures}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {154--163},
     year = {2009},
     volume = {151},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a19/}
}
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V. V. Chugunova. About Circuit Reliability in Full Bases, Containing a Vote Function with Input Inverse Failures. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 2, pp. 154-163. http://geodesic.mathdoc.fr/item/UZKU_2009_151_2_a19/

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[2] Chugunova V. V., “O nadezhnosti skhem v nekotorykh privodimykh polnykh bazisakh”, Izv. vuzov. Povolzhskii region. Fiz.-matem. nauki, 2007, no. 2, 25–37

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