On Reliability of Combinatorial Circuits in Bases Containing Functions with at Most Three Variables

We consider the realization of Boolean functions by combinatorial circuits with gates realizing functions from a complete basis $B$, containing functions with at most three variables. We assume that gates can have inverse faults on the outputs independently with the probability $\varepsilon$ ($\varepsilon\in(0;1/2)$). We describe a set $G$ of Boolean functions depending essentially on three variables, and prove that for almost all Boolean functions the unreliability of asymptotically optimal circuits is asymptotically equal to $\varepsilon$ (when $\varepsilon$ tends to 0) if and only if $G\cap B\ne\emptyset$.