Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Alon, Noga; Kumar, Mrinal; Volk, Ben Lee http://www.dagstuhl.de/lipics License
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Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits

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Abstract

We prove a lower bound of Omega(n^2/log^2 n) on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial f(x_1, ..., x_n). Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff ([Ran Raz et al., 2008]), who proved a lower bound of Omega(n^{4/3}/log^2 n) for the same polynomial. Our improvement follows from an asymptotically optimal lower bound for a generalized version of Galvin's problem in extremal set theory.

BibTeX - Entry

@InProceedings{alon_et_al:LIPIcs:2018:8879,
  author =	{Noga Alon and Mrinal Kumar and Ben Lee Volk},
  title =	{{Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{11:1--11:16},
  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 fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8879},
  URN =		{urn:nbn:de:0030-drops-88799},
  doi =		{10.4230/LIPIcs.CCC.2018.11},
  annote =	{Keywords: Algebraic Complexity, Multilinear Circuits, Circuit Lower Bounds}
}

Keywords: Algebraic Complexity, Multilinear Circuits, Circuit Lower Bounds
Seminar: 33rd Computational Complexity Conference (CCC 2018)
Issue date: 2018
Date of publication: 2018


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