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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 10, Pages 17–24
(Mi ivm1748)
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Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number
O. V. Zubkov Irkutsk State Pedagogical University
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
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
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https://www.mathnet.ru/eng/ivm1748 https://www.mathnet.ru/eng/ivm/y2008/i10/p17
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Abstract page: | 248 | Full-text PDF : | 75 | References: | 35 | First page: | 1 |
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