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.ICALP.2016.33
URN: urn:nbn:de:0030-drops-63126
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6312/
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Kayal, Neeraj ; Saha, Chandan ; Tavenas, Sébastien

An Almost Cubic Lower Bound for Depth Three Arithmetic Circuits

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LIPIcs-ICALP-2016-33.pdf (0.6 MB)

Abstract

We show an almost cubic lower bound on the size of any depth three arithmetic circuit computing an explicit multilinear polynomial in n variables over any field. This improves upon the previously known quadratic lower bound by Shpilka and Wigderson [CCC, 1999].

BibTeX - Entry

@InProceedings{kayal_et_al:LIPIcs:2016:6312,
  author =	{Neeraj Kayal and Chandan Saha and S{\'e}bastien Tavenas},
  title =	{{An Almost Cubic Lower Bound for Depth Three Arithmetic Circuits}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{33:1--33:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6312},
  URN =		{urn:nbn:de:0030-drops-63126},
  doi =		{10.4230/LIPIcs.ICALP.2016.33},
  annote =	{Keywords: arithmetic circuits, depth-3 circuits, shifted partials}
}

Keywords: arithmetic circuits, depth-3 circuits, shifted partials
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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