Maximal number of Boolean functions realized by an initial Boolean automaton with two constant states
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 12-17
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The problem of realization of Boolean functions by initial Boolean automata with two constant states and $n$ inputs is considered. Initial Boolean automaton with two 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 maximum cardinality of set of $n$-ary Boolean functions where $n > 1$ realized by an initial Boolean automaton with two 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 nekotorykh svoistvakh obobschennykh $\alpha$-formul”, Vestn. Mosk. un-ta. Matem. Mekhan., 2013, no. 4, 51–55 | MR | Zbl
[4] 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