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Depth-4 Lower Bounds, Determinantal Complexity : A Unified Approach
[article]

2013
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arXiv
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pre-print

Tavenas has recently proved that any n^O(1)-variate and degree n polynomial in VP can be computed by a depth-4 circuit of size 2^O(√(n) n). So to prove VP not equal to VNP, it is sufficient to show that an explicit polynomial in VNP of degree n requires 2^ω(√(n) n) size depth-4 circuits. Soon after Tavenas's result, for two different explicit polynomials, depth-4 circuit size lower bounds of 2^Ω(√(n) n) have been proved Kayal et al. and Fournier et al. In particular, using combinatorial design

arXiv:1308.1640v4
fatcat:es3qwpss5zhgdgd5dvnxczmehu