About Reliability of Circuits with Faults of Type 0 at the Outputs of Elements in a Full Finite Basis Containing a Special Function

Abstract

We consider a realization of Boolean functions by the circuits from unreliable elements in a full basis B, containing a special function. We assume that all elements of a circuit are exposed to the faults type 0 at the outputs with probability e ∈ (0, 1/2) independently of each other. We prove that almost any Boolean function can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to e with e → 0.