Identity Testing and Lower Bounds for Read- k Oblivious Algebraic Branching Programs
Matthew William Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk · ACM Transactions on Computation Theory · 2018
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/k O ( 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 Õ( n 1−1/2 k −1 ) and needs white box access only to know the order in which the variables appear in the ABP.