License: 
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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2018.11
URN: urn:nbn:de:0030-drops-88799
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8879/
Alon, Noga ;
Kumar, Mrinal ;
Volk, Ben Lee
Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits
Abstract
We prove a lower bound of Omega(n^2/log^2 n) on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial f(x_1, ..., x_n). Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff ([Ran Raz et al., 2008]), who proved a lower bound of Omega(n^{4/3}/log^2 n) for the same polynomial. Our improvement follows from an asymptotically optimal lower bound for a generalized version of Galvin's problem in extremal set theory.
BibTeX - Entry
@InProceedings{alon_et_al:LIPIcs:2018:8879,
author = {Noga Alon and Mrinal Kumar and Ben Lee Volk},
title = {{Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits}},
booktitle = {33rd Computational Complexity Conference (CCC 2018)},
pages = {11:1--11:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-069-9},
ISSN = {1868-8969},
year = {2018},
volume = {102},
editor = {Rocco A. Servedio},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2018/8879},
URN = {urn:nbn:de:0030-drops-88799},
doi = {10.4230/LIPIcs.CCC.2018.11},
annote = {Keywords: Algebraic Complexity, Multilinear Circuits, Circuit Lower Bounds}
}
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Keywords: |
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Algebraic Complexity, Multilinear Circuits, Circuit Lower Bounds |
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Collection: |
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33rd Computational Complexity Conference (CCC 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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04.06.2018 |
