# Collapsing Exact Arithmetic Hierarchies

@inproceedings{Balaji2014CollapsingEA,
title={Collapsing Exact Arithmetic Hierarchies},
author={Nikhil Balaji and Samir Datta},
booktitle={WALCOM},
year={2014}
}
• Published in WALCOM 13 February 2014
• Computer Science, Mathematics
We provide a uniform framework for proving the collapse of the hierarchy $${\sf NC}^1(\mathcal{C})$$ for an exact arithmetic class $$\mathcal{C}$$ of polynomial degree. These hierarchies collapse all the way down to the third level of the AC 0-hierarchy, $${\sf AC^0_3}(\mathcal{C})$$. Our main collapsing exhibits are the classes

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