Abstract
We consider realization of Boolean functions by the circuits composed of unreliable elements in a complete basis B ⊂ B3 (with B3 the set of all Boolean functions of three variables x1, x2, and x3). We assume that, with probability ɛ ∈ (0, 1/2), all elements of a circuit are independently subjected to inverse failures at outputs. All bases are found in which it is possible to realize almost all Boolean functions by the circuits asymptotically optimal in reliability and functioning with unreliability 3ɛ as ɛ → 0. It is proved that there are no other bases B ⊂ B3 like these.
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