Arithmetic Circuit Lower Bounds via MaxRank

@article{Kumar2013ArithmeticCL,
  title={Arithmetic Circuit Lower Bounds via MaxRank},
  author={Mrinal Kumar and Gaurav Maheshwari and Jayalal Sarma},
  journal={ArXiv},
  year={2013},
  volume={abs/1302.3308}
}
We introduce the polynomial coefficient matrix and identify maximum rank of this matrix under variable substitution as a complexity measure for multivariate polynomials. We use our techniques to prove super-polynomial lower bounds against several classes of non-multilinear arithmetic circuits. In particular, we obtain the following results : · As our first main result, we prove that any homogeneous depth-3 circuit for computing the product of d matrices of dimension n ×n requires Ω(nd−1/2d… 
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