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.CCC.2018.12
URN: urn:nbn:de:0030-drops-88772
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8877/
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Carmosino, Marco L. ; Impagliazzo, Russell ; Lovett, Shachar ; Mihajlin, Ivan

Hardness Amplification for Non-Commutative Arithmetic Circuits

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LIPIcs-CCC-2018-12.pdf (0.5 MB)

Abstract

We show that proving mildly super-linear lower bounds on non-commutative arithmetic circuits implies exponential lower bounds on non-commutative circuits. That is, non-commutative circuit complexity is a threshold phenomenon: an apparently weak lower bound actually suffices to show the strongest lower bounds we could desire.
This is part of a recent line of inquiry into why arithmetic circuit complexity, despite being a heavily restricted version of Boolean complexity, still cannot prove super-linear lower bounds on general devices. One can view our work as positive news (it suffices to prove weak lower bounds to get strong ones) or negative news (it is as hard to prove weak lower bounds as it is to prove strong ones). We leave it to the reader to determine their own level of optimism.

BibTeX - Entry

@InProceedings{carmosino_et_al:LIPIcs:2018:8877,
  author =	{Marco L. Carmosino and Russell Impagliazzo and Shachar Lovett and Ivan Mihajlin},
  title =	{{Hardness Amplification for Non-Commutative Arithmetic Circuits}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{12:1--12:16},
  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/2018/8877},
  URN =		{urn:nbn:de:0030-drops-88772},
  doi =		{10.4230/LIPIcs.CCC.2018.12},
  annote =	{Keywords: arithmetic circuits, hardness amplification, circuit lower bounds, non-commutative computation}
}

Keywords: arithmetic circuits, hardness amplification, circuit lower bounds, non-commutative computation
Collection: 33rd Computational Complexity Conference (CCC 2018)
Issue Date: 2018
Date of publication: 04.06.2018

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