Lower Bounds of Algebraic Branching Programs and Layerization

07/14/2020

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by   Christian Engels, et al.

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In this paper we improve the lower bound of Chatterjee et al. (ECCC 2019) to an Ω(n^2) lower bound for unlayered Algebraic Branching Programs. We also study the impact layerization has on Algebraic Branching Programs. We exhibit a polynomial that has an unlayered ABP of size O(n) but any layered ABP has size at least Ω(n√(n)). We exhibit a similar dichotomy in the non-commutative setting where the unlayered ABP has size O(n) and any layered ABP has size at least Ω(nlog n -log^2 n).