Geodesic
Bounds on Shannon functions of lengths of contact closure tests for contact circuits
Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 49-67

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We consider the problem of synthesis of irredundant two-pole contact circuits which implement $n$-place Boolean functions and allow short single fault detection or diagnostic tests of closures of at most $k$ contacts. We prove that the Shannon function of the length of a fault detection test is equal to $n$ for any $n$ and $k$, and that the Shannon function of the length of a diagnostic test is majorized by $n+k(n-2)$ for $n\geqslant 2$.
Keywords: contact circuit, contact closure, Boolean function, fault detection test, diagnostic test, Shannon function. 
@article{DM_2020_32_3_a3,
     author = {K. A. Popkov},
     title = {Bounds on {Shannon} functions of lengths of contact closure tests for contact circuits},
     journal = {Diskretnaya Matematika},
     pages = {49--67},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_3_a3/}
}
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K. A. Popkov. Bounds on Shannon functions of lengths of contact closure tests for contact circuits. Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 49-67. http://geodesic.mathdoc.fr/item/DM_2020_32_3_a3/