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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 10, Pages 17–24 (Mi ivm1748)  

Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number

O. V. Zubkov

Irkutsk State Pedagogical University
References:
Abstract: In this paper we consider noniterated Boolean functions in the basis $\{\&,\vee,-\}$. We obtain the canonical form of the formula for a noniterated function in this basis. We construct the set of such formulas in terms of the variables $x_1,\dots,x_n$ and calculate the number of its elements. Based on these results, we obtain the upper and lower bounds for the number of noniterated Boolean functions of $n$ variables in the basis under consideration.
Keywords: noniterated Boolean function, number of noniterated functions, estimates for the number of noniterated functions.
Received: 03.06.2003
Revised: 02.12.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 10, Pages 13–19
DOI: https://doi.org/10.3103/S1066369X08100022
Bibliographic databases:
UDC: 519.714
Language: Russian
Citation: O. V. Zubkov, “Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 10, 17–24; Russian Math. (Iz. VUZ), 52:10 (2008), 13–19
Citation in format AMSBIB
\Bibitem{Zub08}
\by O.~V.~Zubkov
\paper Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 10
\pages 17--24
\mathnet{http://mi.mathnet.ru/ivm1748}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2528917}
\zmath{https://zbmath.org/?q=an:1182.06006}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 10
\pages 13--19
\crossref{https://doi.org/10.3103/S1066369X08100022}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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