This article is cited in 2 papers

Mathematical Foundations of Reliability of Computing and Control Systems

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

M. A. Alekhina

Penza State University, Penza

Abstract: 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 $\gamma_0$ or $\gamma_1$ and $\varepsilon_0$ or $\varepsilon_1$ 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 $2\varepsilon_0+2\gamma_0+\varepsilon_1+2\gamma_1^2$ for $\gamma_0,\gamma_1,\varepsilon_0,\varepsilon_1\to0$. This estimation is achieved for functions $f\not\in\bigcup_{n=1}^\infty K(n)$ where $K(n)$ is the set of all Boolean functions $\bar x_i\vee h$ and $x_i\wedge\bar h$ for $i\in\{1,\dots,n\}$ and $h$ – an arbitrary Boolean function of variables $x_1,\dots,x_n$.

Keywords: unreliable functional gates, unreliability of circuits, constant failures.

UDC: 519.718

DOI: 10.17223/2226308X/8/37