# A Quadratic Lower Bound for Algebraic Branching Programs

@article{Chatterjee2019AQL, title={A Quadratic Lower Bound for Algebraic Branching Programs}, author={Prerona Chatterjee and Mrinal Kumar and Adrian She and Ben lee Volk}, journal={Electronic Colloquium on Computational Complexity (ECCC)}, year={2019}, volume={26}, pages={170} }

We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results in [K19], which showed a quadratic lower bound for \emph{homogeneous} ABPs computing the same polynomial.
Our proof relies on a notion of depth reduction which is reminiscent of similar statements in the… CONTINUE READING

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