Mathematical Foundations of Reliability of Computing and Control Systems

The reliability of circuits in the basis of unreliable and absolutely reliable gates

M. A. Alekhina, A. E. Lakomkina

Penza State University, Penza

Abstract: The implementation of Boolean functions by circuits in the standard basis containing conjunction, disjunction and inversion is considered. It is assumed that some of the basic gates (e.g. conjunctor) are reliable, and the rest (inverter, disjunctor) are unreliable, i.e., with a probability $\varepsilon\in(0,1/2)$, they are subjected to inverse faults at the outputs. It is also assumed that all unreliable circuit gates get faulty independently of each other. Some answers to the following questions are obtained: what is the unreliability of a circuit, if some of the basic elements are reliable, while others are unreliable?

Keywords: absolutely reliable and unreliable functional gates, reliability of circuits, unreliability of circuits, inverse failures on outputs of gates.

UDC: 519.718