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Approaching the chasm at depth four

Ankit Gupta, Pritish Kamath, Neeraj Kayal, and Ramprasad Saptharishi


Agrawal-Vinay (FOCS 2008) and Koiran (TCS 2012) have recently shown that an exp(√(n) * log2 n)) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of gates having fanin bounded by √(n) translates to super-polynomial lower bound for a general arithmetic circuits computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin.

We show here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by √(n) computing the permanent (or the determinant) must be of size exp(√(n)) .


Publication typeInproceedings
Published inConference on Computational Complexity
AwardsBest Paper Award
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