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 journalArticlepeer-review


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
Article number3
JournalACM Transactions on Computation Theory
Issue number1
StatePublished - Jan 2018


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


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