On the Limits of Depth Reduction at Depth 3 Over Small Finite Fields

@article{Chillara2014OnTL,
  title={On the Limits of Depth Reduction at Depth 3 Over Small Finite Fields},
  author={Suryajith Chillara and Partha Mukhopadhyay},
  journal={ArXiv},
  year={2014},
  volume={abs/1401.0189}
}
In a surprising recent result, Gupta et al. [GKKS13b] have proved that over ℚ any n O(1)-variate and n-degree polynomial in VP can also be computed by a depth three ∑ ∏ ∑ circuit of size \(2^{O(\sqrt{n} \log^{3/2}n)}\) . Over fixed-size finite fields, Grigoriev and Karpinski proved that any ∑ ∏ ∑ circuit that computes the determinant (or the permanent) polynomial of a n×n matrix must be of size 2Ω(n). In this paper, for an explicit polynomial in VP (over fixed-size finite fields), we prove that… 
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