Identity testing and lower bounds for read-k oblivious algebraic branching programs

Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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/kO(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(n1-1/2k-1 ) and needs white box access only to know the order in which the variables appear in the ABP.

Original languageEnglish
Title of host publication31st Conference on Computational Complexity, CCC 2016
EditorsRan Raz
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages30:1-30:25
ISBN (Electronic)9783959770088
DOIs
StatePublished - 1 May 2016
Event31st Conference on Computational Complexity, CCC 2016 - Tokyo, Japan
Duration: 29 May 20161 Jun 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume50
ISSN (Print)1868-8969

Conference

Conference31st Conference on Computational Complexity, CCC 2016
Country/TerritoryJapan
CityTokyo
Period29/05/161/06/16

Keywords

  • Algebraic complexity
  • Derandomization
  • Lower bounds
  • Polynomial identity testing

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