Asymptotically optimal in reliability circuits in two bases under failures of $0$ ($k-1$) type at the outputs of elements

We consider the problem of the realization of $k$-meaning logics ($k\geq 3$) circuits in the two bases: in Rosser–Turkett basis and in its dual basis. We assume that the basic elements are exposed to faults on the outputs: only type $0$ or only type $k-1$, and they go into fault conditions independently. We describe a constructive method for the synthesis of asymptotically optimal reliable circuit for almost any $k$-meaning logic function, we found the upper and lower bounds of circuits unreliability and the class of functions for which the lower bound is true.