Abstract
We consider the implementation of Boolean functions by circuits consisting of unreliable functional gates in the basis which contains only anticonjunction. We assume that each circuit gate is exposed to the faults of type 0 or type 1 at the inputs. The circuits are constructed for all Boolean functions and the upper bound of their unreliability is found which depends only on the probabilities of appearance of type 0 fault and type 1 fault at the gate inputs. We also prove that the found upper bound of the circuits unreliability is asymptotically (for small values of probability) equals the lower bound of the unreliability for almost all Boolean functions.
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Original Russian Text © M.A. Alekhina, V.V. Kurysheva, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 7, pp. 3–9.
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Alekhina, M.A., Kurysheva, V.V. On the circuits reliability in “anticonjunction” basis with constant faults at gate inputs. Russ Math. 60, 1–6 (2016). https://doi.org/10.3103/S1066369X1607001X
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DOI: https://doi.org/10.3103/S1066369X1607001X