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 inJournal of applied and industrial mathematics Vol. 13; no. 4; pp. 746 - 752
Main Author Sergeev, I. S.
Format Journal Article
LanguageEnglish
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
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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.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478919040161