Volume 21, No 4, 2014, P. 12-24

UDC 519.718
M. A. Alekhina and O. Yu. Barsukova
On reliability of circuits realizing ternary logic functions

We consider a realization of the ternary logics functions by the circuits with unreliable functional gates in a full finite basis. It is assumed that gates turn in faulty condition independently and the faults can be arbitrary (e.g., inverse or constant). We describe a class G of ternary logic functions whose circuits can be used to improve the reliability of initial circuits. With inverse faults on the outputs of the basic gates, using functions of the class G constructively we prove that a function different from any variable can be realized with a reliable circuit (we remind that a function equal to a variable can be realized reliably without using functional elements). In particular, if the basis contains at least one function from G, then the proposed circuits are not only reliable, but asymptotically reliability optimal for all functions different from any variable.
Ill. 2, bibliogr. 4.

Keywords: ternary logics function, functional elements circuit, unreliability of a circuit.

Alekhina Marina Anatolievna 1
Barsukova Oxana Yurievna 1

1. Penza State University,
40 Krasnaya St., 440026 Penza, Russia
e-mail: ama@sura.ru, kuzya_7@mail.ru

 © Sobolev Institute of Mathematics, 2015