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Electronic Colloquium on Computational Complexity

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Reports tagged with Restrictions:
TR13-100 | 15th July 2013
Hervé Fournier, Nutan Limaye, Guillaume Malod, Srikanth Srinivasan

Lower bounds for depth $4$ formulas computing iterated matrix multiplication

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 >>>


TR17-187 | 3rd December 2017
Roei Tell

A Note on the Limitations of Two Black-Box Techniques in Quantified Derandomization

The quantified derandomization problem of a circuit class $\mathcal{C}$ with a function $B:\mathbb{N}\rightarrow\mathbb{N}$ is the following: Given an input circuit $C\in\mathcal{C}$ over $n$ bits, deterministically distinguish between the case that $C$ accepts all but $B(n)$ of its inputs and the case that $C$ rejects all but $B(n)$ of its inputs. ... more >>>


TR21-076 | 4th June 2021
Dmitry Sokolov

Pseudorandom Generators, Resolution and Heavy Width

Following the paper of Alekhnovich, Ben-Sasson, Razborov, Wigderson \cite{ABRW04} we call a pseudorandom generator $\mathrm{PRG}\colon \{0, 1\}^n \to \{0, 1\}^m$ hard for for a propositional proof system $\mathrm{P}$ if $\mathrm{P}$ cannot efficiently prove the (properly encoded) statement $b \notin \mathrm{Im}(\mathrm{PRG})$ for any string $b \in \{0, 1\}^m$.

In \cite{ABRW04} authors ... more >>>




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