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Electronic Colloquium on Computational Complexity

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Reports tagged with hitting-set:
TR12-113 | 7th September 2012
Manindra Agrawal, Chandan Saha, Nitin Saxena

Quasi-polynomial Hitting-set for Set-depth-$\Delta$ Formulas

We call a depth-$4$ formula $C$ $\textit{ set-depth-4}$ if there exists a (unknown) partition $X_1\sqcup\cdots\sqcup X_d$ of the variable indices $[n]$ that the top product layer respects, i.e. $C(\mathbf{x})=\sum_{i=1}^k {\prod_{j=1}^{d} {f_{i,j}(\mathbf{x}_{X_j})}}$ $ ,$ where $f_{i,j}$ is a $\textit{sparse}$ polynomial in $\mathbb{F}[\mathbf{x}_{X_j}]$. Extending this definition to any depth - we call ... more >>>

TR13-186 | 27th December 2013
Nitin Saxena

Progress on Polynomial Identity Testing - II

We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.

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TR17-163 | 2nd November 2017
Michael Forbes, Amir Shpilka

A PSPACE Construction of a Hitting Set for the Closure of Small Algebraic Circuits

In this paper we study the complexity of constructing a hitting set for $\overline{VP}$, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given ... more >>>

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