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 sparse polynomials with bounded individual degree and the class of their factors. In particular we obtain the following algorithmic and structural results:
1. A deterministic polynomial-time algorithm for finding all the sparse divisors of a sparse polynomial with bounded individual degree. As part of this, we establish ... more >>>
A symbolic determinant under rank-one restriction computes a polynomial of the form $\det(A_0 + A_1y_1 + \ldots + A_ny_n)$, where $A_0, A_1, \ldots, A_n$ are square matrices over a field $\mathbb{F}$ and $\rank(A_i) = 1$ for each $i \in [n]$. This class of polynomials has been studied extensively, since the ... more >>>
We construct a universal decompressor $U$ for plain Kolmogorov complexity $\mathrm{C}_U$ such that the Halting Problem cannot be decided by any polynomial-time oracle machine with access to the set of random strings $R_{\mathrm{C}_U} = \{x : \mathrm{C}_U(x) \ge |x|\}$. This result resolves a problem posed by Eric Allender regarding the ... more >>>
