Geodesic
Asymptotically optimal in reliability circuits in two bases under failures of $0$ ($k-1$) type at the outputs of elements
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 3-12

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We consider the problem of the realization of $k$-meaning logics ($k\geq 3$) circuits in the two bases: in Rosser–Turkett basis and in its dual basis. We assume that the basic elements are exposed to faults on the outputs: only type $0$ or only type $k-1$, and they go into fault conditions independently. We describe a constructive method for the synthesis of asymptotically optimal reliable circuit for almost any $k$-meaning logic function, we found the upper and lower bounds of circuits unreliability and the class of functions for which the lower bound is true.
Keywords: $k$-meaning logics function, unreliable functional gates, reliability and unreliability of circuit, synthesis of circuits composed of unreliable gates, fault of type $0$, fault of type $k-1$. 
@article{IVM_2018_5_a0,
     author = {M. A. Alekhina and O. Yu. Barsukova},
     title = {Asymptotically optimal in reliability circuits in two bases under failures of $0$ ($k-1$) type at the outputs of elements},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--12},
     publisher = {mathdoc},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_5_a0/}
}
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%J Izvestiâ vysših učebnyh zavedenij. Matematika
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M. A. Alekhina; O. Yu. Barsukova. Asymptotically optimal in reliability circuits in two bases under failures of $0$ ($k-1$) type at the outputs of elements. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 3-12. http://geodesic.mathdoc.fr/item/IVM_2018_5_a0/