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Mat. Zametki, 2012, Volume 92, Issue 2, Pages 181–191 (Mi mz7833)  

Realization of Boolean Functions by Formulas in Continuous Bases Containing a Continuum of Constants

Ya. V. Vegner, S. B. Gashkov

M. V. Lomonosov Moscow State University

Abstract: For an arbitrary Boolean function of $n$ variables, we show how to construct formulas of complexity $O(2^{n/2})$ in the bases
$$ \{x-y,xy,|x|\} \cup [0,1],\qquad \{x-y,x*y,2x,|x|\} \cup [0,1], $$
where ${x*y=\max(-1,\min(1,x))\max(-1,\min(1,y))}$. The obtained estimates are, in general, order-sharp.

Keywords: Boolean function, complexity of the realization of Boolean functions, Shannon function, Lipschitz condition, continuous basis, almost-finite basis

DOI: https://doi.org/10.4213/mzm7833

Full text: PDF file (483 kB)
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English version:
Mathematical Notes, 2012, 92:2, 166–175

Bibliographic databases:

UDC: 512.563
Received: 26.04.2009
Revised: 19.12.2010

Citation: Ya. V. Vegner, S. B. Gashkov, “Realization of Boolean Functions by Formulas in Continuous Bases Containing a Continuum of Constants”, Mat. Zametki, 92:2 (2012), 181–191; Math. Notes, 92:2 (2012), 166–175

Citation in format AMSBIB
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