On the design of switching circuits admitting small detection test sets
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 110-115
Voir la notice du chapitre de livre provenant de la source Math-Net.Ru
It is established that for an arbitrary nonconstant Boolean function $f(x_1,\dots,x_n)$ there exists a testable switching circuit, a) which is a circuit realizing the system $(f,\bar f)$ and admitting the single fault detection test set of power $O(n)$, b) which is a circuit realizing the function $f(x_1,\dots,x_n)\oplus x_{n+1}$ and admitting the single fault detection test set of power $O(n)$. It is also proved that almost all Boolean functions $f(x_1,\dots, x_n)$ can be realized by switching circuits which admit small detection test sets (test sets of power $O(n)$) under homogeneous faults (closures or breakings).
Keywords:
Boolean function, switching circuit, detection test set.
@article{UZKU_2014_156_3_a10,
author = {D. S. Romanov},
title = {On the design of switching circuits admitting small detection test sets},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {110--115},
publisher = {mathdoc},
volume = {156},
number = {3},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a10/}
}
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%0 Journal Article %A D. S. Romanov %T On the design of switching circuits admitting small detection test sets %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2014 %P 110-115 %V 156 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a10/ %G ru %F UZKU_2014_156_3_a10
D. S. Romanov. On the design of switching circuits admitting small detection test sets. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 110-115. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a10/