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Electronic Colloquium on Computational Complexity

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All reports by Author Sébastien Tavenas:

TR17-021 | 11th February 2017
Neeraj Kayal, Vineet Nair, Chandan Saha, Sébastien Tavenas

Reconstruction of full rank Algebraic Branching Programs

An algebraic branching program (ABP) A can be modelled as a product expression $X_1\cdot X_2\cdot \dots \cdot X_d$, where $X_1$ and $X_d$ are $1 \times w$ and $w \times 1$ matrices respectively, and every other $X_k$ is a $w \times w$ matrix; the entries of these matrices are linear forms ... more >>>

TR16-132 | 23rd August 2016
Mitali Bafna, Satyanarayana V. Lokam, Sébastien Tavenas, Ameya Velingker

On the Sensitivity Conjecture for Read-k Formulas

Various combinatorial/algebraic parameters are used to quantify the complexity of a Boolean function. Among them, sensitivity is one of the simplest and block sensitivity is one of the most useful. Nisan (1989) and Nisan and Szegedy (1991) showed that block sensitivity and several other parameters, such as certificate complexity, decision ... more >>>

TR16-006 | 22nd January 2016
Neeraj Kayal, Chandan Saha, Sébastien Tavenas

An almost Cubic Lower Bound for Depth Three Arithmetic Circuits

Revisions: 2

We show an $\Omega \left(\frac{n^3}{(\ln n)^2}\right)$ lower bound on the size of any depth three ($\SPS$) arithmetic circuit computing an explicit multilinear polynomial in $n$ variables over any field. This improves upon the previously known quadratic lower bound by Shpilka and Wigderson.

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TR15-181 | 13th November 2015
Neeraj Kayal, Chandan Saha, Sébastien Tavenas

On the size of homogeneous and of depth four formulas with low individual degree

Let $r \geq 1$ be an integer. Let us call a polynomial $f(x_1, x_2,\ldots, x_N) \in \mathbb{F}[\mathbf{x}]$ as a multi-$r$-ic polynomial if the degree of $f$ with respect to any variable is at most $r$ (this generalizes the notion of multilinear polynomials). We investigate arithmetic circuits in which the output ... more >>>

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