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

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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Bibliographic Details
Published in:Journal of applied and industrial mathematics Vol. 13; no. 4; pp. 746 - 752
Main Author: Sergeev, I. S.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.10.2019
Springer Nature B.V
Subjects:
Boolean
Boolean algebra
Boolean functions
Complexity
Mathematics
Mathematics and Statistics
complexity
depth
monotone function
Boolean formula
ISSN:1990-4789, 1990-4797
Online Access:Get full text
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Description
Summary: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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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478919040161