Unreliability of circuits in case of constant failures on inputs and outputs of gates

We consider the implementation of Boolean functions by circuits of unreliable functional elements in the basis containing only Sheffer stroke. It is assumed that each of the circuit elements is exposed to type 0 or type 1 failures in its inputs and outputs with probabilities 70 or y ₁ and e ₀ or e ₁ respectively. It is shown that any Boolean function can be so implemented by a such circuit that the asymptotic estimate of its unreliability is no more than 2e ₀ + 2y ₀ + e ₁ + 2y 00 for 7 ₀,7 ₁,e ₀,e ₁ ^ 0. This estimation is achieved for functions f е U K(n) where K(n) is _ n=1 the set of all Boolean functions x^ V h and xj Л h for i е {1,..., n} and h - an arbitrary Boolean function of variables x ₁,..., x _n.

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