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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.365
URN: urn:nbn:de:0030-drops-39481
URL: http://drops.dagstuhl.de/opus/volltexte/2013/3948/
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Capelli, Florent ; Durand, Arnaud ; Mengel, Stefan

The arithmetic complexity of tensor contractions

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Abstract

We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits. This gives a natural and robust characterization of this complexity class that despite its naturalness is not very well understood so far.

BibTeX - Entry

@InProceedings{capelli_et_al:LIPIcs:2013:3948,
  author =	{Florent Capelli and Arnaud Durand and Stefan Mengel},
  title =	{{The arithmetic complexity of tensor contractions}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{365--376},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3948},
  URN =		{urn:nbn:de:0030-drops-39481},
  doi =		{10.4230/LIPIcs.STACS.2013.365},
  annote =	{Keywords: algebraic complexity, arithmetic circuits, tensor calculus}
}

Keywords: algebraic complexity, arithmetic circuits, tensor calculus
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 18.02.2013


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