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On reliability of circuits over the basis {x ∨ y ∨ z, x & y & z, } under single-type constant faults at inputs of elements
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M. A. Alekhina
Published/Copyright:
March 1, 2006
We consider realisation of Boolean functions over the basis {x ∨ y ∨ z, x & y & z, 
} by circuits of unreliable functional elements which are subject to single-type constant faults at inputs of the elements. Let γ
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(x1, . . . , xn)
such that the functions xi, i = 1, 2, . . . , 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 γ3 as
γ → 0.
Published Online: 2006-03-01
Published in Print: 2006-03-01
Copyright 2006, Walter de Gruyter
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