Geodesic
Estimates for lengths of check and diagnostic tests of functional elements
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 6, pp. 73-89.

Voir la notice de l'article provenant de la source Math-Net.Ru

We examine problems of check of repair and state diagnosis of $N$ functional elements which realize a given Boolean function $f(x_1,\ldots,x_n)$ in their perfect states by means of composition of one-output circuits and observation of values produced by these circuits on any value sets of input variables. Random constant faults on outputs of functional elements are permitted; at the same time, it is assumed that not more than $k$ elements are faulted, where $k$ is a natural number that does not rank over $N$. It is needed to minimize a number of circuits required for check of repair and determination of states of all elements. It is shown that no more than $k$ circuits are required for each $f,N$, and $k$. For functions $f$ of special kind, necessary and sufficient conditions that $k$ circuits are enough for check of repair and state diagnosis of all elements are obtained. Ill. 3, bibliogr. 2.
Keywords: functional element, fault, check test
Mots-clés : circuit, diagnostic test. 
@article{DA_2014_21_6_a5,
     author = {K. A. Popkov},
     title = {Estimates for lengths of check and diagnostic tests of functional elements},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {73--89},
     publisher = {mathdoc},
     volume = {21},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2014_21_6_a5/}
}
TY  - JOUR
AU  - K. A. Popkov
TI  - Estimates for lengths of check and diagnostic tests of functional elements
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2014
SP  - 73
EP  - 89
VL  - 21
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2014_21_6_a5/
LA  - ru
ID  - DA_2014_21_6_a5
ER  - 
%0 Journal Article
%A K. A. Popkov
%T Estimates for lengths of check and diagnostic tests of functional elements
%J Diskretnyj analiz i issledovanie operacij
%D 2014
%P 73-89
%V 21
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2014_21_6_a5/
%G ru
%F DA_2014_21_6_a5
K. A. Popkov. Estimates for lengths of check and diagnostic tests of functional elements. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 6, pp. 73-89. http://geodesic.mathdoc.fr/item/DA_2014_21_6_a5/

[1] Lupanov O. B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, Izd-vo MGU, M., 1984, 139 pp.

[2] Redkin N. P., Nadëzhnost i diagnostika skhem, Izd-vo MGU, M., 1992, 191 pp.