In the last few days, a Denial of Service attack was launched on universities in Israel, leading the administrators of the Israel Academic network to block access to it from the global internet. Consequently, websites such as ECCC have been accessible only from within the Israeli and European academic networks.
It seems that this blocking was just removed, and we hope it will not be put back in the future.
Needless to say, deciding on such blocking is not in our control, but we do apologize for this disruption of service.
We study factoring algorithms for general sparse polynomials and sparse polynomials of bounded individual degree and prove the following results.
1. We give a deterministic polynomial-time algorithm which takes as input an $n$-variate $s$-sparse polynomial $f$ of bounded individual degree $d$ and outputs a list of circuits which contains ...
more >>>
We study depth-$5$ algebraic circuits over small finite fields with restricted fan-in of the top product gates. We show that there exists an explicit degree-$d$ polynomial $P(\mathbf{x})$ such that any $\Sigma \Pi^{[\mathrm{poly(d)}]} \Sigma \Pi \Sigma$ circuit, computing $P(\mathbf{x})$, over a small finite field, requires size $2^{\Omega(\sqrt{d})}$. Our work builds upon ... more >>>
We establish the first super-polynomial quantum advantage for the tolerant junta testing problem in the adaptive setting. Specifically, we show that within a certain parameter regime, tolerant $k$-junta testing with high precision can be solved using $\mathrm{poly}(k)$ quantum queries, whereas any classical algorithm requires at least $k^{\Omega(\log k)}$ queries.
The ... more >>>
