Abstract
We describe a general method of proving degree lower bounds for conical juntas (nonnegative combinations of conjunctions) that compute recursively defined boolean functions. Such lower bounds are known to carry over to communication complexity. We give two applications:
- AND-OR trees. We show a near-optimal ~Omega(n^{0.753...}) randomised communication lower bound for the recursive NAND function (a.k.a. AND-OR tree). This answers an open question posed by Beame and Lawry.
- Majority trees. We show an Omega(2.59^k) randomised communication lower bound for the 3-majority tree of height k. This improves over the state-of-the-art already in the context of randomised decision tree complexity.
BibTeX - Entry
@InProceedings{gs_et_al:LIPIcs:2016:5849,
author = {Mika G{\"o}{\"o}s and T. S. Jayram},
title = {{A Composition Theorem for Conical Juntas}},
booktitle = {31st Conference on Computational Complexity (CCC 2016)},
pages = {5:1--5:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-008-8},
ISSN = {1868-8969},
year = {2016},
volume = {50},
editor = {Ran Raz},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5849},
URN = {urn:nbn:de:0030-drops-58497},
doi = {10.4230/LIPIcs.CCC.2016.5},
annote = {Keywords: Composition theorems, conical juntas}
}
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Keywords: |
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Composition theorems, conical juntas |
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Collection: |
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31st Conference on Computational Complexity (CCC 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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19.05.2016 |
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)