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.FSTTCS.2020.6
URN: urn:nbn:de:0030-drops-132472
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13247/
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Shpilka, Amir

On Some Recent Advances in Algebraic Complexity (Invited Talk)

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LIPIcs-FSTTCS-2020-6.pdf (0.2 MB)

Abstract

Algebraic complexity is the field studying the intrinsic difficulty of algebraic problems in an algebraic model of computation, most notably arithmetic circuits. It is a very natural model of computation that attracted a large amount of research in the last few decades, partially due to its simplicity and elegance, but mostly because of its importance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, deciding whether P = BPP and more, will be easier to solve for arithmetic circuits.
In this talk I will give the basic definitions, explain the main questions and how they relate to their Boolean counterparts, and discuss what I view as promising approaches to tackling the most fundamental problems in the field.

BibTeX - Entry

@InProceedings{shpilka:LIPIcs:2020:13247,
  author =	{Amir Shpilka},
  title =	{{On Some Recent Advances in Algebraic Complexity (Invited Talk)}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{6:1--6:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Nitin Saxena and Sunil Simon},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13247},
  URN =		{urn:nbn:de:0030-drops-132472},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.6},
  annote =	{Keywords: Algebraic Complexity, Arithmetic Circuits, Polynomial Identity Testing}
}

Keywords: Algebraic Complexity, Arithmetic Circuits, Polynomial Identity Testing
Collection: 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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