All reports by Author Guillaume Malod:

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TR19-100
| 31st July 2019
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Hervé Fournier, Guillaume Malod, Maud Szusterman, Sébastien Tavenas#### Nonnegative rank measures and monotone algebraic branching programs

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TR16-094
| 6th June 2016
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Guillaume Lagarde, Guillaume Malod#### Non-commutative computations: lower bounds and polynomial identity testing

Comments: 1

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TR15-022
| 9th February 2015
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Nutan Limaye, Guillaume Malod, Srikanth Srinivasan#### Lower bounds for non-commutative skew circuits

Revisions: 1

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TR14-163
| 29th November 2014
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Arnaud Durand, Meena Mahajan, Guillaume Malod, Nicolas de Rugy-Altherre, Nitin Saurabh#### Homomorphism polynomials complete for VP

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TR13-100
| 15th July 2013
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Hervé Fournier, Nutan Limaye, Guillaume Malod, Srikanth Srinivasan#### Lower bounds for depth $4$ formulas computing iterated matrix multiplication

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TR11-134
| 9th October 2011
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Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff#### Separating multilinear branching programs and formulas

Hervé Fournier, Guillaume Malod, Maud Szusterman, Sébastien Tavenas

Inspired by Nisan's characterization of noncommutative complexity (Nisan 1991), we study different notions of nonnegative rank, associated complexity measures and their link with monotone computations. In particular we answer negatively an open question of Nisan asking whether nonnegative rank characterizes monotone noncommutative complexity for algebraic branching programs. We also prove ... more >>>

Guillaume Lagarde, Guillaume Malod

In the setting of non-commutative arithmetic computations, we define a class of circuits that gener-

alize algebraic branching programs (ABP). This model is called unambiguous because it captures the

polynomials in which all monomials are computed in a similar way (that is, all the parse trees are iso-

morphic).

We ...
more >>>

Nutan Limaye, Guillaume Malod, Srikanth Srinivasan

Nisan (STOC 1991) exhibited a polynomial which is computable by linear sized non-commutative circuits but requires exponential sized non-commutative algebraic branching programs. Nisan's hard polynomial is in fact computable by linear sized skew circuits (skew circuits are circuits where every multiplication gate has the property that all but one of ... more >>>

Arnaud Durand, Meena Mahajan, Guillaume Malod, Nicolas de Rugy-Altherre, Nitin Saurabh

The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant ... more >>>

Hervé Fournier, Nutan Limaye, Guillaume Malod, Srikanth Srinivasan

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 >>>

Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff

This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be computationally equivalent to two basic tools in linear algebra: iterated matrix multiplication and the determinant. We compare the computational power of ... more >>>