On reliability of circuits with type 0 failures at elements outputs in a full finite basis containing a linear function of two variables and generalized disincent

Background. The increasing complexity of modern information processing, transmission and storage systems highlights the requirement for reliability and control of various control and computing systems. The article is devoted to the actual problem of constructing asymptotically optimal in reliability circuits that implement Boolean functions and function with a trivial unreliability estimate, for faults of type 0 at the outputs of elements in the basis containing an essential linear function of two variables and a generalized two-place disjunction. Element faults are assumed statistically independent. The goal of the work is to get answers to the following questions: Is it possible to implement an arbitrary Boolean function in the bases under consideration by an asymptotically optimal in terms of reliability scheme and what is the unreliability of this scheme? Materials and methods. Methods of the theory of reliability of operating systems are used in work. Results and conclusions. It is proved that in the considered bases for almost all Boolean functions, asymptotically optimal in reliability schemes function with unreliability asymptotically equal to $\epsilon$ as $\epsilon \to 0$ (here, $\epsilon$ is the probability of failure of the basis element). These results can be used in the synthesis of reliable circuits, as well as in the design of technical systems to increase their reliability.