Year: 2020
Type: preprint
Abstract: 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 $Ω(n\sqrt{n})$. 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 $Ω(n\log n -\log^2 n)$.
Source: arXiv (Cornell University)
Author: Engels, Christian
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3042666635