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: Contribution to journalArticle

Abstract

Read-k oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ABP). 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 (US)
Article number3
JournalACM Transactions on Computation Theory
Volume10
Issue number1
DOIs
StatePublished - Jan 2018

Keywords

  • Algebraic circuits
  • Algebraic complexity theory
  • Lower bounds
  • Polynomial identity testing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Fingerprint Dive into the research topics of 'Identity testing and lower bounds for read-k oblivious algebraic branching programs'. Together they form a unique fingerprint.

  • Cite this