Geodesic
On implementation of some systems of elementary conjunctions in the class of separating contact circuits
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 47-60

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We show that the system of elementary conjunctions $\Omega_{n,2^k} = {K_0,\ldots,K_{2^{k} -1}}$ such that each conjunction depends essentially on $n$ variables and corresponds to some codeword of a linear $(n, k)$-code can be implemented by a separating contact circuit of complexity at most $2^{k+1} + 4k(n - k) - 2$. We also show that if a contact $(1, 2^k)$-terminal network is separating and implements the system of elementary conjunctions $\Omega_{n,2^k}$, then the number of contacts in it is at least $2^{k+1} - 2$.
Keywords: elementary conjunction, contact circuits, separating circuits, complexity of circuits. 
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     author = {E. G. Krasulina},
     title = {On implementation of some systems of elementary conjunctions in the class of separating contact circuits},
     journal = {Diskretnaya Matematika},
     pages = {47--60},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_4_a4/}
}
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E. G. Krasulina. On implementation of some systems of elementary conjunctions in the class of separating contact circuits. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 47-60. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a4/