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DOI: 10.4230/LIPIcs.CCC.2016.30
URN: urn:nbn:de:0030-drops-58255
URL: http://drops.dagstuhl.de/opus/volltexte/2016/5825/
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Anderson, Matthew ; Forbes, Michael A. ; Saptharishi, Ramprasad ; Shpilka, Amir ; Volk, Ben Lee

Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs

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Abstract

Read-k oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs). In this work, we give an exponential lower bound of exp(n/k^{O(k)}) on the width of any read-k oblivious ABP computing some explicit multilinear polynomial f that is computed by a polynomial size depth-3 circuit. We also study the polynomial identity testing (PIT) problem for this model and obtain a white-box subexponential-time PIT algorithm. The algorithm runs in time 2^{~O(n^{1-1/2^{k-1}})} and needs white box access only to know the order in which the variables appear in the ABP.

BibTeX - Entry

@InProceedings{anderson_et_al:LIPIcs:2016:5825,
  author =	{Matthew Anderson and Michael A. Forbes and Ramprasad Saptharishi and Amir Shpilka and Ben Lee Volk},
  title =	{{Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{30:1--30:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Ran Raz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5825},
  URN =		{urn:nbn:de:0030-drops-58255},
  doi =		{10.4230/LIPIcs.CCC.2016.30},
  annote =	{Keywords: Algebraic Complexity, Lower Bounds, Derandomization, Polynomial Identity Testing}
}

Keywords: Algebraic Complexity, Lower Bounds, Derandomization, Polynomial Identity Testing
Seminar: 31st Conference on Computational Complexity (CCC 2016)
Issue Date: 2016
Date of publication: 18.05.2016


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