This article is cited in 1 paper

Asymptotically optimal in reliability circuits in two bases under failures of $0$ ($k-1$) type at the outputs of elements

M. A. Alekhina^a, O. Yu. Barsukova<sup>b

a</sup> Penza State Technological University, 1a/1 Baidukov passage / Garagin str., Penza, 440039 Russia
^b Penza State University, 40 Krasnaya str., Penza, 440026 Russia

Abstract: We consider the problem of the realization of $k$-meaning logics ($k\geq 3$) circuits in the two bases: in Rosser–Turkett basis and in its dual basis. We assume that the basic elements are exposed to faults on the outputs: only type $0$ or only type $k-1$, and they go into fault conditions independently. We describe a constructive method for the synthesis of asymptotically optimal reliable circuit for almost any $k$-meaning logic function, we found the upper and lower bounds of circuits unreliability and the class of functions for which the lower bound is true.

Keywords: $k$-meaning logics function, unreliable functional gates, reliability and unreliability of circuit, synthesis of circuits composed of unreliable gates, fault of type $0$, fault of type $k-1$.

UDC: 519.718

Received: 28.02.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:5, 1–9

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