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On reliability of circuits over the basis \(\{x \vee y \vee z, x \, \&\, y\, \& \, z, \bar x\}\) under single-type constant faults at inputs of elements. (English. Russian original) Zbl 1121.94032
Discrete Math. Appl. 16, No. 2, 195-203 (2006); translation from Diskretn. Mat. 18, No. 1, 116-125 (2006).
Summary: We consider realisation of Boolean functions over the basis \(\{x \vee y \vee z, x\, \& \, y\, \& \, z, \bar x\}\) by circuits of unreliable functional elements which are subject to single-type constant faults at inputs of the elements. Let \(\gamma \) be the probability of a fault at an input of an element. By the unreliability of a circuit is meant the greatest probability of error at its output. In this paper, we find the asymptotically best realisation of an arbitrary Boolean function \(f(x _{1},\cdots, x_{n} )\) such that the functions \(x_{i}\) , \(i = 1, 2,\cdots ,n\), are realised absolutely reliably, the constants 0 and 1 are realised as reliably as we wish, and the remaining functions are realised with unreliability asymptotically equal to \(\gamma ^{3}\) as \(\gamma \rightarrow 0\).
MSC:
94C12 Fault detection; testing in circuits and networks
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References:
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