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This article is cited in 1 scientific paper (total in 1 paper)
On the reliability of schemes in the basis $\{x\vee y\vee z,x\mathbin{\&}y\mathbin{\&}z,\bar{x}\}$ with single-type constant faults at the inputs of the element
M. A. Alekhina
Abstract:
We consider realisation of Boolean functions over the basis
$\{x \vee y \vee z, x\mathbin{\&}y \mathbin{\&}z, \bar{x}\}$
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 $f(x_1,\dots,x_n)$ such that
the functions $x_i$, $i=1,2,\dots,n$, 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 $\gamma\to 0$.
This research was supported by the Scientific Program
‘Universities of Russia,’ grant 04.01.032.
Received: 05.11.2004
Citation:
M. A. Alekhina, “On the reliability of schemes in the basis $\{x\vee y\vee z,x\mathbin{\&}y\mathbin{\&}z,\bar{x}\}$ with single-type constant faults at the inputs of the element”, Diskr. Mat., 18:1 (2006), 116–125; Discrete Math. Appl., 16:2 (2006), 195–203
Linking options:
https://www.mathnet.ru/eng/dm36https://doi.org/10.4213/dm36 https://www.mathnet.ru/eng/dm/v18/i1/p116
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