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Electronic Colloquium on Computational Complexity

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All reports by Author Hervé Fournier:

TR15-118 | 23rd July 2015
Hervé Fournier, Nutan Limaye, Meena Mahajan, Srikanth Srinivasan

The shifted partial derivative complexity of Elementary Symmetric Polynomials

We continue the study of the shifted partial derivative measure, introduced by Kayal (ECCC 2012), which has been used to prove many strong depth-4 circuit lower bounds starting from the work of Kayal, and that of Gupta et al. (CCC 2013).

We show a strong lower bound on the dimension ... more >>>

TR13-100 | 15th July 2013
Hervé Fournier, Nutan Limaye, Guillaume Malod, Srikanth Srinivasan

Lower bounds for depth $4$ formulas computing iterated matrix multiplication

We study the arithmetic complexity of iterated matrix multiplication. We show that any multilinear homogeneous depth $4$ arithmetic formula computing the product of $d$ generic matrices of size $n \times n$, IMM$_{n,d}$, has size $n^{\Omega(\sqrt{d})}$ as long as $d \leq n^{1/10}$. This improves the result of Nisan and Wigderson (Computational ... more >>>

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