Geodesic
Asymptotically optimal in unreliability circuits in~the~basis~consisting of the Webb function in $P_3$ under~faults of type $2$ at the outputs of elements
Prikladnaâ diskretnaâ matematika, no. 1 (2020), pp. 22-29.

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We consider the realization of ternary logic functions by circuits from unreliable elements in full 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-type constant faults of type $2$ at the outputs. It is proved that any function of ternary logic can be realized by an asymptotically optimal in reliability circuit functioning with unreliability which is asymptotically no more $3\varepsilon$ with $\varepsilon\rightarrow 0$. A class of functions is found (it contains almost all ternary logic functions), each of which cannot be implemented by a circuit whose unreliability is asymptotically less $3\varepsilon$ with $\varepsilon\rightarrow 0$. Thus, it is proved that almost any function of ternary logic can be implemented by an asymptotically optimal on reliability circuit operating with unreliability which is asymptotically equal to $3\varepsilon$ with $\varepsilon\rightarrow 0$.
Keywords: ternary logic functions, unreliable functional elements, reliability and unreliability of circuit, synthesis of circuits from unreliable elements, faults at outputs of elements. 
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     title = {Asymptotically optimal in unreliability circuits in~the~basis~consisting of the {Webb} function in $P_3$ under~faults of type $2$ at the outputs of elements},
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O. Yu. Barsukova; M. A. Alekhina. Asymptotically optimal in unreliability circuits in~the~basis~consisting of the Webb function in $P_3$ under~faults of type $2$ at the outputs of elements. Prikladnaâ diskretnaâ matematika, no. 1 (2020), pp. 22-29. http://geodesic.mathdoc.fr/item/PDM_2020_1_a2/

[1] Vinogradov Yu. A., “About the synthesis of ternary logic circuits”, Math. Problems of Cybernetics, 3, Nauka Publ., M., 1991, 187–198 (in Russian)

[2] Barsukova O. Yu., Synthesis of reliable schemes that implement two-valued and three-valued logics functions, PhD Thesis, Penza, 2014, 87 pp. (in Russian)

[3] Alekhina M. A., Barsukova O. Yu., “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”, Prikladnaya Diskretnaya Matematika, 2019, no. 44, 56–64