License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.13
URN: urn:nbn:de:0030-drops-101066
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10106/
Bhrushundi, Abhishek ;
Hosseini, Kaave ;
Lovett, Shachar ;
Rao, Sankeerth
Torus Polynomials: An Algebraic Approach to ACC Lower Bounds
Abstract
We propose an algebraic approach to proving circuit lower bounds for ACC^0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC^0 and ACC^0 can be reformulated in this framework, implying that ACC^0 can be approximated by low-degree torus polynomials. Furthermore, as a step towards proving ACC^0 lower bounds for the majority function via our approach, we show that MAJORITY cannot be approximated by low-degree symmetric torus polynomials. We also pose several open problems related to our framework.
BibTeX - Entry
@InProceedings{bhrushundi_et_al:LIPIcs:2018:10106,
author = {Abhishek Bhrushundi and Kaave Hosseini and Shachar Lovett and Sankeerth Rao},
title = {{Torus Polynomials: An Algebraic Approach to ACC Lower Bounds}},
booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
pages = {13:1--13:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-095-8},
ISSN = {1868-8969},
year = {2018},
volume = {124},
editor = {Avrim Blum},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/10106},
URN = {urn:nbn:de:0030-drops-101066},
doi = {10.4230/LIPIcs.ITCS.2019.13},
annote = {Keywords: Circuit complexity, ACC, lower bounds, polynomials}
}
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Keywords: |
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Circuit complexity, ACC, lower bounds, polynomials |
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Collection: |
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10th Innovations in Theoretical Computer Science Conference (ITCS 2019) |
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Issue Date: |
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2018 |
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Date of publication: |
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08.01.2019 |
