Arithmetic Circuits: A Chasm at Depth Four

@article{Agrawal2008ArithmeticCA,
  title={Arithmetic Circuits: A Chasm at Depth Four},
  author={Manindra Agrawal and V. Vinay},
  journal={2008 49th Annual IEEE Symposium on Foundations of Computer Science},
  year={2008},
  pages={67-75}
}
We show that proving exponential lower bounds on depth four arithmetic circuits imply exponential lower bounds for unrestricted depth arithmetic circuits. In other words, for exponential sized circuits additional depth beyond four does not help. We then show that a complete black-box derandomization of identity testing problem for depth four circuits with multiplication gates of small fanin implies a nearly complete derandomization of general identity testing. 
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