On the reliability of circuits in some full bases (in P₃) with inverse faults at the gate outputs

We consider the realization of ternary logic functions by circuits from unreliable functional elements in full finite bases B₁ and B₂, the first of which is the dual one to Rosser - Turkett basis, and the second one is the dual basis to the basis consisting of Webb's function. We assume that the circuit elements are exposed to inverse faults with probability p at element outputs independently. We have obtained the following results: in the basis B₁, 1) any function from P₃ can be realized by a circuit with unreliability that is asymptotically (for small p) not more than 6p; 2) for almost any function, such a circuit is asymptotically optimal to reliability and operates with the unreliability asymptotically equalled 6p for small p; in the basis B₂, almost any function can be realized by a reliable circuit that operates with the unreliability that is asymptotically not more than 8p and asymptotically not less than 6p for small p.

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