Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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