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Diskretnaya Matematika, 2009, Volume 21, Issue 2, Pages 102–111
DOI: https://doi.org/10.4213/dm1050
(Mi dm1050)
 

On reliability of circuits over the bases $\{\sim,\&,\oplus\}$, $\{\sim,\&,0\}$, $\{\oplus,\&,1\}$, $\{\oplus,\vee,1\}$ in the case of faults of type 0 at the outputs of elements

M. A. Alekhina
References:
Abstract: In the case of faults of type 0 at the outputs of elements, it is proved that in the bases $\{\sim,\&,\oplus\}$, $\{\sim,\&,0\}$, $\{\oplus,\&,1\}$, $\{\oplus,\vee,1\}$ almost all Boolean functions can be realised by asymptotically best (optimal) with respect to the reliability circuits functioning with unreliability $P(S)\sim\gamma$ as $\gamma\to0$, where $\gamma$ is the probability of the faulty state of an element.
Received: 26.12.2005
Revised: 27.04.2007
English version:
Discrete Mathematics and Applications, 2009, Volume 19, Issue 1, Pages 37–46
DOI: https://doi.org/10.1515/DMA.2009.002
Bibliographic databases:
UDC: 519.7
Language: Russian
Citation: M. A. Alekhina, “On reliability of circuits over the bases $\{\sim,\&,\oplus\}$, $\{\sim,\&,0\}$, $\{\oplus,\&,1\}$, $\{\oplus,\vee,1\}$ in the case of faults of type 0 at the outputs of elements”, Diskr. Mat., 21:2 (2009), 102–111; Discrete Math. Appl., 19:1 (2009), 37–46
Citation in format AMSBIB
\Bibitem{Ale09}
\by M.~A.~Alekhina
\paper On reliability of circuits over the bases $\{\sim,\&,\oplus\}$, $\{\sim,\&,0\}$, $\{\oplus,\&,1\}$, $\{\oplus,\vee,1\}$ in the case of faults of type~0 at the outputs of elements
\jour Diskr. Mat.
\yr 2009
\vol 21
\issue 2
\pages 102--111
\mathnet{http://mi.mathnet.ru/dm1050}
\crossref{https://doi.org/10.4213/dm1050}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2562231}
\elib{https://elibrary.ru/item.asp?id=20730290}
\transl
\jour Discrete Math. Appl.
\yr 2009
\vol 19
\issue 1
\pages 37--46
\crossref{https://doi.org/10.1515/DMA.2009.002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-63849085125}
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  • https://doi.org/10.4213/dm1050
  • https://www.mathnet.ru/eng/dm/v21/i2/p102
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    Дискретная математика
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