Geodesic
Estimates for the number of Boolean functions realized by an initial Boolean automaton with three constant states
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2017), pp. 19-28 
L. N. Sysoeva. Estimates for the number of Boolean functions realized by an initial Boolean automaton with three constant states. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2017), pp. 19-28. http://geodesic.mathdoc.fr/item/VMUMM_2017_2_a3/
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     title = {Estimates for the number of {Boolean} functions realized by an initial {Boolean} automaton with three constant states},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of realization of Boolean functions by initial Boolean automata with constant states and $n$ inputs is considered. Initial Boolean automaton with constant states and $n$ inputs is an initial automaton with output such that in all states output functions are $n$-ary constant Boolean functions $0$ or $1$. The exact value of the maximum number of $n$-ary Boolean functions, where $n > 1$, realized by an initial Boolean automaton with three constant states and $n$ inputs is obtained.

[1] Yablonskii S.V., Vvedenie v diskretnuyu matematiku, Vysshaya shkola, M., 2006 | MR

[2] A. B. Ugolnikov (otv. red.), Konspekt lektsii O. B. Lupanova po kursu “Vvedenie v matematicheskuyu logiku”, Izd-vo TsPI pri mekh.-mat. f-te MGU, M., 2007

[3] Sysoeva L.N., “O realizatsii bulevykh funktsii obobschennymi $\alpha$-formulami”, Uch. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 156:3 (2014), 116–122 | MR

[4] Sysoeva L.N., “Maksimalnoe chislo bulevykh funktsii, porozhdaemykh initsialnym avtomatom s dvumya konstantnymi sostoyaniyami”, Trudy IX Mezhdunar. konf. (Moskva i Podmoskove, 20–22 maya 2015 g.), eds. V.B. Alekseev, D.S. Romanov, B.R. Danilov, MAKS Press, M., 2015, 239–241

[5] Sysoeva L.N., “O nekotorykh svoistvakh obobschennykh $\alpha$-formul”, Vestn. Mosk. un-ta. Matem. Mekhan., 2013, no. 4, 51–55 | MR | Zbl