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JOURNALS // Prikladnaya Diskretnaya Matematika. Supplement // Archive

Prikl. Diskr. Mat. Suppl., 2014 Issue 7, Pages 113–115 (Mi pdma186)

Mathematical Foundations of Reliability of Computing and Control Systems

About basises with unreliability coefficient 5

A. V. Vasin

Penza State University, Penza

Abstract: Realizations of Boolean functions by the circuits composed of unreliable elements in some complete basises are considered. It is assumed that, with probability $\varepsilon\in(0,1/2)$, all elements of a circuit independently of each other are subjected to inverse failures at the outputs. It is proved that, for all considered basises, it is possible to realize almost all Boolean functions by the circuits being asymptotically optimal by reliability and functioning with the unreliability $5\varepsilon$ as $\varepsilon\to0$.

Keywords: unreliable functional elements, circuits asymptotically optimal with respect to reliability, inverse failures on outputs of elements, synthesis of circuits composed of unreliable elements.

UDC: 519.718



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