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Diskr. Mat., 2009 Volume 21, Issue 2, Pages 102–111 (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


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.

UDC: 519.7

Received: 26.12.2005
Revised: 27.04.2007

DOI: 10.4213/dm1050


 English version:
Discrete Mathematics and Applications, 2009, 19:1, 37–46

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© Steklov Math. Inst. of RAS, 2024