Short complete diagnostic tests for circuits with~one~additional input in the standard basis
Prikladnaâ diskretnaâ matematika, no. 2 (2022), pp. 104-112.

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

We prove that each monotone (antimonotone) Boolean function in $n$ variables can be modeled by a logic circuit with one additional input in the basis “conjunction, disjunction, negation” allowing a complete diagnostic test with length no more than $n+2$ (no more than $n+1$, respectively) relative to constant faults of type $1$ at outputs of logic gates.
Keywords: logic circuit, stuck-at fault, complete diagnostic test, Boolean function.
@article{PDM_2022_2_a5,
     author = {K. A. Popkov},
     title = {Short complete diagnostic tests for circuits with~one~additional input in the standard basis},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {104--112},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2022_2_a5/}
}
TY  - JOUR
AU  - K. A. Popkov
TI  - Short complete diagnostic tests for circuits with~one~additional input in the standard basis
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2022
SP  - 104
EP  - 112
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2022_2_a5/
LA  - ru
ID  - PDM_2022_2_a5
ER  - 
%0 Journal Article
%A K. A. Popkov
%T Short complete diagnostic tests for circuits with~one~additional input in the standard basis
%J Prikladnaâ diskretnaâ matematika
%D 2022
%P 104-112
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2022_2_a5/
%G ru
%F PDM_2022_2_a5
K. A. Popkov. Short complete diagnostic tests for circuits with~one~additional input in the standard basis. Prikladnaâ diskretnaâ matematika, no. 2 (2022), pp. 104-112. http://geodesic.mathdoc.fr/item/PDM_2022_2_a5/

[1] S. V. Yablonskii, “Nadezhnost i kontrol upravlyayuschikh sistem”, Materialy Vsesoyuznogo seminara po diskretnoi matematike i ee prilozheniyam (Moskva, 31 yanvarya–2 fevralya 1984 g.), Izd-vo MGU, M., 1986, 7–12

[2] S. V. Yablonskii, “Nekotorye voprosy nadezhnosti i kontrolya upravlyayuschikh sistem”, Matematicheskie voprosy kibernetiki, 1, Nauka, M., 1988, 5–25

[3] N. P. Redkin, Nadezhnost i diagnostika skhem, Izd-vo MGU, M., 1992, 192 pp.

[4] K. A. Popkov, “Nizhnie otsenki dlin polnykh diagnosticheskikh testov dlya skhem i vkhodov skhem”, Prikladnaya diskretnaya matematika, 2016, no. 4 (34), 65–73 | Zbl

[5] N. P. Redkin, “K voprosu o dline diagnosticheskikh testov dlya skhem”, Matematicheskie zametki, 102:4 (2017), 624–627 | Zbl

[6] S. A. Lozhkin, Lektsii po osnovam kibernetiki, uchebnoe posobie dlya studentov, Izdatelskii otdel f-ta VMiK MGU, M., 2004, 251 pp.

[7] S. V. Yablonskii, Vvedenie v diskretnuyu matematiku, Nauka, M., 1986, 384 pp. | MR

[8] K. A. Popkov, O vozmozhnostyakh postroeniya legkotestiruemykh kontaktnykh skhem i skhem iz funktsionalnykh elementov, dis. ... d-ra fiz. mat. nauk, M., 2021, 377 pp.

[9] A. D. Korshunov, “O chisle monotonnykh bulevykh funktsii”, Problemy kibernetiki, 38, Nauka, M., 1981, 5–108