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Diskretnyi Analiz i Issledovanie Operatsii, 2019, Volume 26, Issue 4, Pages 108–120
DOI: https://doi.org/10.33048/daio.2019.26.643 (Mi da939) 		 
On a relation between the depth and complexity of monotone Boolean formulas

I. S. Sergeev

Scientific and Research Institute «Kvant», 15 Chetvyortyi Likhachyovskii Lane, 125438 Moscow, Russia
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DOI: https://doi.org/10.33048/daio.2019.26.643
Abstract: We present a sequence of monotone Boolean functions whose depth over the basis $\{\vee,\wedge\}$ is $c>1.06$ times greater than the logarithm of the formula complexity. Tab. 1, bibliogr. 24.
Keywords: Boolean formula, depth, complexity, monotone function.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00294_а
This research is supported by the Russian Foundation for Basic Research (Project 19–01–00294-a).
Received: 26.12.2018
Revised: 01.06.2019
Accepted: 05.06.2019
Document Type: Article
UDC: 519.7
Language: Russian
Citation: I. S. Sergeev, “On a relation between the depth and complexity of monotone Boolean formulas”, Diskretn. Anal. Issled. Oper., 26:4 (2019), 108–120
Citation in format AMSBIB
\Bibitem{Ser19}
\by I.~S.~Sergeev
\paper On a relation between the depth and complexity of~monotone Boolean formulas
\jour Diskretn. Anal. Issled. Oper.
\yr 2019
\vol 26
\issue 4
\pages 108--120
\mathnet{http://mi.mathnet.ru/da939}
\crossref{https://doi.org/10.33048/daio.2019.26.643}
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