Synthesis of Reliable Circuits in the Basis Consisting of the Webb Function in P4 and P5

Abstract

It is considered the realization of k-valued logic functions (k = 4 and k = 5) by the circuits of unreliable functional elements in a complete basis consisting of the Webb function. It is assumed that the basis elements pass into faulty states independently of each other and the faults are such that each of the incorrect values appears at the output of the basis element with the same probability.

It is shown that any function of k-valued logic (k = 4 and k = 5) can be realized by the reliable circuit, the upper bound is obtained, and moreover the probability of the appearance of the fault is bounded by a constant.