Geodesic
On the complexity of implementation of characteristic functions of the spheres by circuits of functional elements
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2022), pp. 18-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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For characteristic functions of spheres, an asymptotics for the complexity of their implementation by circuits of functional elements in the basis $\{\&,\vee,-\}$ is established; the characteristic function of a sphere with the center at the vertex $\tilde\sigma=(\sigma_1,\ldots,\sigma_n)$, $\sigma_1,\ldots,\sigma_n\in\{0,1\}$, is the Boolean function equal to one on all those and only those sets of values of variables each of which differs from the vertex $\tilde\sigma$ only in one digit. 
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N. P. Red'kin. On the complexity of implementation of characteristic functions of the spheres by circuits of functional elements. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2022), pp. 18-20. http://geodesic.mathdoc.fr/item/VMUMM_2022_3_a3/

[1] Lupanov O.B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, Izd-vo MGU, M., 1984

[2] Redkin N.P., “Minimalnye kontaktnye skhemy dlya kharakteristicheskikh funktsii sfer”, Diskretn. matem., 32:3 (2020), 68–75 | MR

[3] Grinchuk M.I., “O monotonnoi slozhnosti porogovykh funktsii”, Metody diskretnogo analiza v teorii grafov i slozhnosti, 1992, no. 52, 41–48 | MR

[4] Redkin N.P., “Minimalnye kontaktnye skhemy dlya simmetricheskikh porogovykh funktsii”, Matem. zametki, 108:3 (2020), 397–411 | MR | Zbl

[5] Redkin N.P., “Dokazatelstvo minimalnosti nekotorykh skhem iz funktsionalnykh elementov”, Problemy kibernetiki, 23, Nauka, M., 1970, 83–101 | MR