All reports by Author Guillaume Lagarde:

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TR18-180
| 3rd November 2018
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Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann, Olivier Serre#### Lower bounds for arithmetic circuits via the Hankel matrix

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TR18-038
| 21st February 2018
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Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann#### Tight Bounds using Hankel Matrix for Arithmetic Circuits with Unique Parse Trees

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TR17-077
| 30th April 2017
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Guillaume Lagarde, Nutan Limaye, Srikanth Srinivasan#### Lower Bounds and PIT for Non-Commutative Arithmetic circuits with Restricted Parse Trees

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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

Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann, Olivier Serre

We study the complexity of representing polynomials by arithmetic circuits in both the commutative and the non-commutative settings. Our approach goes through a precise understanding of the more restricted setting where multiplication is not associative, meaning that we distinguish $(xy)z$ from $x(yz)$.

Our first and main conceptual result is a ... more >>>

Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann

This paper studies lower bounds for arithmetic circuits computing (non-commutative) polynomials. Our conceptual contribution is an exact correspondence between circuits and weighted automata: algebraic branching programs are captured by weighted automata over words, and circuits with unique parse trees by weighted automata over trees.

The key notion for understanding the ... more >>>

Guillaume Lagarde, Nutan Limaye, Srikanth Srinivasan

We investigate the power of Non-commutative Arithmetic Circuits, which compute polynomials over the free non-commutative polynomial ring $\mathbb{F}\langle x_1,\dots,x_N \rangle$, where variables do not commute. We consider circuits that are restricted in the ways in which they can compute monomials: this can be seen as restricting the families of parse ... 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 >>>