Ran Raz

We prove a lower bound of $\Omega(m^2 \log m)$ for the size of

any arithmetic circuit for the product of two matrices,

over the real or complex numbers, as long as the circuit doesn't

use products with field elements of absolute value larger than 1

(where $m \times m$ is ...
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Rocco Servedio, Emanuele Viola

We highlight the special case of Valiant's rigidity

problem in which the low-rank matrices are truth-tables

of sparse polynomials. We show that progress on this

special case entails that Inner Product is not computable

by small $\acz$ circuits with one layer of parity gates

close to the inputs. We then ...
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Zeev Dvir, Alexander Golovnev, Omri Weinstein

We show that static data structure lower bounds in the group (linear) model imply semi-explicit lower bounds on matrix rigidity. In particular, we prove that an explicit lower bound of $t \geq \omega(\log^2 n)$ on the cell-probe complexity of linear data structures in the group model, even against arbitrarily small ... more >>>

Lijie Chen, Xin Lyu

In this work we prove that there is a function $f \in \textrm{E}^\textrm{NP}$ such that, for every sufficiently large $n$ and $d = \sqrt{n}/\log n$, $f_n$ ($f$ restricted to $n$-bit inputs) cannot be $(1/2 + 2^{-d})$-approximated by $\textrm{F}_2$-polynomials of degree $d$. We also observe that a minor improvement ...
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