About the reliability of circuits in the basis containing a special function

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