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A Note on Depth Reduction : A Simple Proof of the Chasm

Agrawal and Vinay [AV08] showed how any subexponential arithmetic circuit can be thought of as a depth four subexponential arithmetic circuit. This unexpected depth reduction to constant depth is in contrast to curcuits in the Boolean setting. The resulting circuit size in this simulation was more carefully analyzed by Korian [Koi12] and subsequently by Tavenas [Tav13]. We provide a simple proof of this chain of results. We then abstract the main ingredient to apply it to formulas and constant depth circuits.