Geodesic
About reliability of circuits in the basis consisting of~the Webb function in $P_k$ under failures of 0 type and~$k-1$~type at the outputs of elements
Prikladnaâ diskretnaâ matematika, no. 2 (2019), pp. 58-66

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We consider the realization of $k$-valued logics ($k > 3$) functions by circuits of unreliable functional elements in the complete basis consisting of the Webb function. We assume that elements of the circuit pass to fault states independently of each other, and they are exposed to single constant faults of type $0$ or $k-1$ at their outputs. It is constructively proved that, under faults of type 0, almost any function of $k$-valued logics can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to unreliability of one basis element; under faults of type $k-1$, any function of $k$-valued logics can be implemented by an reliable circuit which functions with unreliability asymptotically no more than three times of the unreliability of one basic element. The obtained results are valid in a dual (with respect to the permutation generating by the Lukashevich function) basis for single-type constant faults of type $ k-1 $ and type 0 respectively.
Keywords: $k$-valued logics functions, unreliable functional elements, reliability and unreliability of circuit, synthesis of circuits from unreliable elements, faults at outputs of elements. 
@article{PDM_2019_2_a4,
     author = {M. A. Alekhina and O. Yu. Barsukova},
     title = {About reliability of circuits in the basis consisting of~the {Webb} function in $P_k$ under failures of 0 type and~$k-1$~type at the outputs of elements},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {58--66},
     publisher = {mathdoc},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2019_2_a4/}
}
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M. A. Alekhina; O. Yu. Barsukova. About reliability of circuits in the basis consisting of~the Webb function in $P_k$ under failures of 0 type and~$k-1$~type at the outputs of elements. Prikladnaâ diskretnaâ matematika, no. 2 (2019), pp. 58-66. http://geodesic.mathdoc.fr/item/PDM_2019_2_a4/