The reliability of circuits in Rosser–Turkett basis (in $P_3$) with faults of type $0$ at the outputs of gates

We consider the realization of ternary logic functions by circuits from unreliable functional elements in Rosser–Turkett basis. We assume that all circuit elements are exposed to faults of type $0$ at the outputs and they pass to fault states independently with probability $\varepsilon$ ($\varepsilon<1/2$). We have obtained the following results: 1) any function of ternary logic can be realized by a circuit with unreliability that is asymptotically not more than $\varepsilon$ for small $\varepsilon$; 2) for any function except the constant $0$ and the variable $ x_i$ ($i\in\mathbb N$), such a circuit is asymptotically optimal to reliability and operates with the unreliability asymptotically equalled $\varepsilon$ for small $\varepsilon$; 3) the functions $0$ and $x_i $ can be realized absolutely reliably.