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

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