About the Reliability of Circuits in the Complete Finite Basis Containing an Essential Linear Function

We consider the the implementation of Boolean functions by circuits from unreliable functional elements in a complete finite basis, which contains a linear function essentially dependent on at least two variables. We assume that all elements of a circuit are exposed to the faults of 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.