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

We consider a problem of the realization of <italic>k</italic>-valued logics functions (<italic>k</italic> ≥ 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 <italic>k</italic> − 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 <italic>k</italic>-valued logic, we found the upper and lower bounds of circuits unreliability and the class of functions for which the lower bounds are true. [ABSTRACT FROM AUTHOR]