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URN: urn:nbn:de:0030-drops-90582
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Towards Blackbox Identity Testing of Log-Variate Circuits

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Abstract

Derandomization of blackbox identity testing reduces to extremely special circuit models. After a line of work, it is known that focusing on circuits with constant-depth and constantly many variables is enough (Agrawal,Ghosh,Saxena, STOC'18) to get to general hitting-sets and circuit lower bounds. This inspires us to study circuits with few variables, eg. logarithmic in the size s.
We give the first poly(s)-time blackbox identity test for n=O(log s) variate size-s circuits that have poly(s)-dimensional partial derivative space; eg. depth-3 diagonal circuits (or Sigma wedge Sigma^n). The former model is well-studied (Nisan,Wigderson, FOCS'95) but no poly(s2^n)-time identity test was known before us. We introduce the concept of cone-closed basis isolation and prove its usefulness in studying log-variate circuits. It subsumes the previous notions of rank-concentration studied extensively in the context of ROABP models.

BibTeX - Entry

@InProceedings{forbes_et_al:LIPIcs:2018:9058,
  author =	{Michael A. Forbes and Sumanta Ghosh and Nitin Saxena},
  title =	{{Towards Blackbox Identity Testing of Log-Variate Circuits}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9058},
  URN =		{urn:nbn:de:0030-drops-90582},
  doi =		{10.4230/LIPIcs.ICALP.2018.54},
  annote =	{Keywords: hitting-set, depth-3, diagonal, derandomization, polynomial identity testing, log-variate, concentration, cone closed, basis isolation}
}

Keywords: hitting-set, depth-3, diagonal, derandomization, polynomial identity testing, log-variate, concentration, cone closed, basis isolation
Seminar: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue date: 2018
Date of publication: 04.07.2018


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