An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

Neeraj Kayal; Nutan Limaye; Chandan Saha; Srikanth Srinivasan

An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

Neeraj Kayal ,
Nutan Limaye ,
Chandan Saha ,
Srikanth Srinivasan

Foundations of Computer Science (FOCS) | October 2014

Published by IEEE - Institute of Electrical and Electronics Engineers

Invited to Special Issue of SICOMP journal

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We show here a N^sqrt(d) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d³ in our case) with 0,1-coefficients such that any homogeneous depth four arithmetic formula computing such an f must have size at least N^sqrt(d).

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