Asymptotically Optimal in Reliability Circuits in Two Bases Under Failures of 0 (k − 1) Type at the Outputs of Elements

Abstract

We consider a problem of the realization of k-valued logics functions (k ≥ 3) by circuits in two bases: in the Rosser–Turkett basis and in its dual basis. We assume that the basis gates are exposed to faults at outputs: only of type 0 or only of type k − 1, and they pass into faulty states independently of each other. We describe a constructive method for the synthesis of an asymptotically optimal reliable circuit for almost any function of k-valued logic, we found the upper and lower bounds of circuits unreliability and the class of functions for which the lower bounds are true.