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Electronic Colloquium on Computational Complexity

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All reports by Author Guillaume Lagarde:

TR18-180 | 3rd November 2018
Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann, Olivier Serre

Lower bounds for arithmetic circuits via the Hankel matrix

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 >>>

TR18-038 | 21st February 2018
Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann

Tight Bounds using Hankel Matrix for Arithmetic Circuits with Unique Parse Trees

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 >>>

TR17-077 | 30th April 2017
Guillaume Lagarde, Nutan Limaye, Srikanth Srinivasan

Lower Bounds and PIT for Non-Commutative Arithmetic circuits with Restricted Parse Trees

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 >>>

TR16-094 | 6th June 2016
Guillaume Lagarde, Guillaume Malod

Non-commutative computations: lower bounds and polynomial identity testing

Comments: 1

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-
We ... more >>>

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