SYNTHESIS OF RELIABLE CIRCUITS AT CONSTANT FAILURES AT GATES’ INPUTS AND OUTPUTS

Alekhina Marina Anatol'evna, Doctor of physical and mathematical sciences, professor, head of sub-department of discrete mathematics, Penza State University (40 Krasnaya street, Penza, Russia), alehina@pnzgu.ru

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Background. The article considers realization of Boolean functions by circuits made of unreliable functional gates in a basis, consisting of a single function – the Sheffer function. The problem of synthesis of reliable circuits, realizing Boolean functions at constant failures of similar type (for example, only of 0 type at gates’ inputs) was solved by the author in many articles, but unlike the previous articles, this one considers a model where each circuit gate may be subject to constant fail-ures of 4 types at once: type 0 and type 1 at inputs and outputs (with different probabilities). One should also note that having a proper choice of parameters the model describes inverse failures of gates at inputs and (or) outputs. The aim of the work is to build reliable circuits and to obain the upper and lower values of circuit unreliability.
Materials and methods. When building reliable circuits the author used the previously known methods of synthesis and obtainment of unreliability values.
Results. The author obtained the upper value of circuit unreliability, described the K function class, containing almost all Boolean functions, and proved the lower value of unreliability of circuits, realizing the functions of the given class. For K class functions the author built a circuit, the upper and lower unreliability values of which are asymptotically equal. The obtained results may be used in design of technical systems for their reliability improvement.
Conclusions. Almost any Boolean function may be realized by a circuit, the lower and upper unreliability values of which are asymptotically equal.

unreliable functional gates, reliability of circuits, unreliability of circuits, constant failures of type 0 and type 1 at gates’ inputs and outputs.

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