Geodesic
Synthesis of reliable circuits in the basis consisting of the Webb function in $P_k$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 15-28

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We consider the realization of $k$-meaning logics $(k > 3)$ functions by the circuits from unreliable gates in the complete basis, consisting of the Webb function. We assume that the basic gates pass into faulty states independently of each other and the faults are such that each of the incorrect values appears at the output of the basis gate with the same probability.Previously we developed methods for the synthesis of reliable circuits for $k \in \{3, 4, 5\}$. In this article we show that for $ k \ge 6$ any $k$-meaning logic functions can be realized by an reliable circuit, we offer two methods of the synthesis of reliable circuits and we make a comparison of the upper bounds for unreliability of constructed circuits, which are obtained with the help of these methods.The obtained results are valid in the dual (with respect to the permutation generated by the Lukashevich function) basis for the same faults.
Keywords: $k$-meaning logics functions, unreliable functional gates, reliability and unreliability of circuit, synthesis of circuits from unreliable gates, faults at outputs of gates. 
@article{IVM_2019_7_a1,
     author = {M. A. Alekhina and O. Yu. Barsukova},
     title = {Synthesis of reliable circuits in the basis consisting of the {Webb} function in $P_k$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--28},
     publisher = {mathdoc},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_7_a1/}
}
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M. A. Alekhina; O. Yu. Barsukova. Synthesis of reliable circuits in the basis consisting of the Webb function in $P_k$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 15-28. http://geodesic.mathdoc.fr/item/IVM_2019_7_a1/