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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 4, Pages 12–24 (Mi da781)  

This article is cited in 5 scientific papers (total in 5 papers)

On reliability of circuits realizing ternary logic functions

M. A. Alekhina, O. Yu. Barsukova

Penza State University, 40 Krasnaya St., 440026 Penza, Russia

Abstract: We consider a realization of the ternary logics functions by the circuits with unreliable functional gates in a full finite basis. It is assumed that gates turn in faulty condition independently and the faults can be arbitrary (e.g., inverse or constant). We describe a class $G$ of ternary logic functions whose circuits can be used to improve the reliability of initial circuits. With inverse faults on the outputs of the basic gates, using functions of the class $G$ constructively we prove that a function different from any variable can be realized with a reliable circuit (we remind that a function equal to a variable can be realized reliably without using functional elements). In particular, if the basis contains at least one function from $G$, then the proposed circuits are not only reliable, but asymptotically reliability optimal for all functions different from any variable. Ill. 2, bibliogr. 13.

Keywords: ternary logics function, functional elements circuit, unreliability of a circuit.

Full text: PDF file (285 kB)
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Bibliographic databases:
UDC: 519.718
Received: 11.11.2013
Revised: 21.02.2014

Citation: M. A. Alekhina, O. Yu. Barsukova, “On reliability of circuits realizing ternary logic functions”, Diskretn. Anal. Issled. Oper., 21:4 (2014), 12–24

Citation in format AMSBIB
\Bibitem{AleBar14}
\by M.~A.~Alekhina, O.~Yu.~Barsukova
\paper On reliability of circuits realizing ternary logic functions
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 4
\pages 12--24
\mathnet{http://mi.mathnet.ru/da781}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3289217}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. A. Alekhina, O. Yu. Barsukova, “Nadezhnost skhem v bazise Rossera–Turketta (v $P_3$) pri neispravnostyakh tipa $0$ na vykhodakh elementov”, PDM. Prilozhenie, 2017, no. 10, 124–126  mathnet  crossref
    2. M. A. Alekhina, O. Yu. Barsukova, “Otsenki nenadezhnosti skhem v bazise Rossera–Turketta (v $P_3$) pri neispravnostyakh tipa $0$ na vykhodakh elementov”, PDM, 2017, no. 37, 62–75  mathnet  crossref
    3. M. Alekhina, O. Barsukova, A. Moiseev, “Asymptotically optimal reliable circuits in Rosser–Turkett basis (in $P_k$)”, Lobachevskii J. Math., 38:1 (2017), 62–72  crossref  mathscinet  zmath  isi  scopus
    4. M. Alekhina, O. Barsukova, “Upper bound of the circuits unreliability in a complete finite basis (in $P_3$ ) with arbitrary faults of elements”, Lobachevskii J. Math., 39:1, SI (2018), 13–19  crossref  mathscinet  zmath  isi  scopus
    5. 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”, Russian Math. (Iz. VUZ), 62:5 (2018), 1–9  mathnet  crossref  isi
  • Дискретный анализ и исследование операций
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