We consider the realization of Boolean functions by the circuits of unreliable elements in a complete finite basis containing some pairs of functions. We assume that all elements of a circuit are exposed to the faults type 0 at the outputs with probability \(\varepsilon \in (0,1/2)\) 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 \(\varepsilon\) with \(\varepsilon \to 0\).

中文翻译：

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关于包含某些函数对的完全有限基础中的元素输出在类型0失效下电路的可靠性

我们考虑由不可靠元素的电路在包含一些函数对的完全有限的基础上实现布尔函数。我们假设电路的所有元件在输出处都以彼此独立的概率\（\ varepsilon \ in（0,1 / 2）\）处于故障类型0 。我们证明了，几乎所有布尔函数都可以通过可靠性电路中的渐近最优实现，其中不可靠性渐近等于\（\ varepsilon \）和\（\ varepsilon \ to 0 \）。