Geodesic
Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 99-116

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The following results are proved: 1) any nonconstant Boolean function may be implemented by an irredundant circuit of gates in the basis $\{x\,$ $\overline x,x\oplus y\oplus z\}$ admitting a single fault detection test of length at most 2 with respect to arbitrary stuck-at faults at outputs of gates, 2) there exists a six-place Boolean function $\psi$ such that any nonconstant Boolean function may be implemented by an irredundant circuit of gates in the basis $\{\psi\}$ admitting a single diagnostic test of length at most 3 with respect to arbitrary stuck-at faults at outputs of gates.
Keywords: circuit of gates, stuck-at fault, single fault detection test, single diagnostic test. 
@article{DM_2018_30_3_a8,
     author = {K. A. Popkov},
     title = {Short single tests for circuits with arbitrary stuck-at faults at outputs of gates},
     journal = {Diskretnaya Matematika},
     pages = {99--116},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_3_a8/}
}
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K. A. Popkov. Short single tests for circuits with arbitrary stuck-at faults at outputs of gates. Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 99-116. http://geodesic.mathdoc.fr/item/DM_2018_30_3_a8/