An algebraic branching program (ABP) A can be modelled as a product expression X_1\cdot X_2\cdot \dots \cdot X_d, where X_1 and X_d are 1 \times w and w \times 1 matrices respectively, and every other X_k is a w \times w matrix; the entries of these matrices are linear forms ... more >>>

We show an exponential separation between two well-studied models of algebraic computation, namely read-once oblivious algebraic branching programs (ROABPs) and multilinear depth three circuits. In particular we show the following:

1. There exists an explicit n-variate polynomial computable by linear sized multilinear depth three circuits (with only two product gates) ... more >>>