Circuits to Raise Reliability

Abstract

Let us consider circuits of functional elements that in a certain sense can be said to “vote.” Voting consists of the following: in a circle of radius k the set (0, 0, ..., 0) realized by the circuit of the function takes on the value 0, while in a circle of the same radius the set (1, 1, ..., 1) takes the value 1; in this case we say that the circuit “corrects k errors.” This type of circuit must be used in the synthesis of self-correcting circuits made of functional elements [1]. The circuits considered here are built of 𝓔_µ elements, realizing the function ${h_{\mu }}\left( {{x_{1}},...,{\kern 1pt} {\kern 1pt} {x_{{\mu + 1}}}} \right) = {\kern 1pt} \mathop{V}\limits_{{i = 1}}^{{\mu + 1}} {x_{1}}{x_{2}}{\kern 1pt} ...{\kern 1pt} {x_{{i - 1}}}{x_{{i + 1}}}{\kern 1pt} ...{\kern 1pt} {x_{{\mu + 1}}}$. From the set of all circuits that correct k errors we separate the subset of circuits in which the output of each element, different from the output of the whole circuit, is connected to one input of a certain element.

Original article submitted April 15, 1968