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On a Relation Between the Depth and Complexity of Monotone Boolean Formulas

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Abstract

We present a sequence of monotone Boolean functions whose depth over the basis {∧, ∨} is c > 1.06 times greater than the logarithm of the formula complexity.

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Acknowledgment

The author is grateful to the referee for a careful reading of the article and a number of remarks and suggestions that substantially improved the quality of exposition.

Funding

The author was supported by the Russian Foundation for Basic Research (project no. 19-01-00294-a).

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Authors and Affiliations

  1. Scientific and Research Institute Kvant, Chetvyortyi Likhachyovskii per. 15, Moscow, 125438, Russia

    I. S. Sergeev

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  1. I. S. Sergeev
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Correspondence to I. S. Sergeev.

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Dedicated to the memory of ValeriiMikhailovich Khrapchenko

Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 4, pp. 108–120.

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Sergeev, I.S. On a Relation Between the Depth and Complexity of Monotone Boolean Formulas. J. Appl. Ind. Math. 13, 746–752 (2019). https://doi.org/10.1134/S1990478919040161

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  • DOI: https://doi.org/10.1134/S1990478919040161

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