Geodesic
Asymptotics for the Complexity of Boolean Functions with Small Number of Ones
Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 257-263.

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The class $F_{n,k}$ of Boolean functions consisting of all functions of $n$ variables each of which outputs $1$ at exactly $k$ $n$-tuples of values of the variables is considered. For small $k$, for example, for $k\ln n$, an asymptotics for the complexity of implementation of every function in $F_{n,k}$ by a circuit of functional elements in an irredundant basis containing $x\to y$ and $\overline{x\to y}$ is found.
Keywords: Boolean function, complexity of a function.
Mots-clés : circuit 
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N. P. Red'kin. Asymptotics for the Complexity of Boolean Functions with Small Number of Ones. Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 257-263. http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a8/

[1] K. E. Shennon, Raboty po teorii informatsii i kibernetike, IL, M., 1963

[2] O. B. Lupanov, Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, Izd-vo Mosk. un-ta, Moskva, 1984

[3] B. I. Finikov, “Ob odnom semeistve klassov funktsii algebry logiki i ikh realizatsii v klasse $\Pi$-skhem”, Dokl. AN SSSR, 115:2 (1957), 247–248 | MR | Zbl

[4] N. P. Redkin, “O slozhnosti bulevykh funktsii s malym chislom edinits”, Diskret. matem., 16:4 (2004), 20–31 | DOI | MR | Zbl

[5] E. S. Gorelik, “O slozhnosti realizatsii elementarnykh kon'yunktsii i diz'yunktsii v bazise $\{x/y\}$”, Problemy kibernetiki, 26, Nauka, Moskva, 1973, 27–36 | MR

[6] G. A. Kochergina, “O slozhnosti realizatsii elementarnykh kon'yunktsii i diz'yunktsii skhemami v nekotorykh polnykh bazisakh”, Matematicheskie voprosy kibernetiki, 11, Fizmatlit, M., 2002, 219–246 | MR

[7] N. P. Redkin, “O slozhnosti realizatsii bulevykh funktsii s malym chislom edinits”, Materialy XIII Mezhdunarodnogo seminara “Diskretnaya matematika i ee prilozheniya” imeni akademika O. B. Lupanova" (Moskva, 17–22 iyunya 2019 g.), Izd-vo mekhaniko-matematicheskogo fakulteta MGU, M., 2019, 23–26