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KIAM Preprint № 49, Moscow, 2021
Authors: Popkov K.A.
On self-correcting logic circuits of unreliable gates
Abstract:
The following statements are proved: 1) for any integer m ≥ 3 there is a basis consisting of Boolean functions of no more than m variables, in which any Boolean function can be implemented by a logic circuit of unreliable gates that self-corrects relative to certain faults in an arbitrary number of gates; 2) for any positive integer k there are bases consisting of Boolean functions of no more than two variables, in each of which any Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to certain faults in no more than k gates; 3) there is a functionally complete basis consisting of Boolean functions of no more than two variables, in which almost no Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to at least some faults in no more than one gate.
Keywords:
logic circuit, self-correction, unreliable gate, Boolean function
Publication language: russian,  pages: 18
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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