Residual-String Equality, denoted $\text{ResStringEq}$, is the property consisting of all pairs of strings over $\{0,1,*\}$ that are equal after deleting all `$*$' symbols from them. This property was first introduced by Fischer, Magniez, and Starikovskaya (SODA 2018), who used it to show a lower bound on testing the $\text{Dyck}$ languages, ... more >>>

Let $G=[n]$ and let an unknown binary operation $*:G\times G\to G$ be given by oracle access to its multiplication table. The tester is given $n$ explicitly as part of its input. A query chooses $x,y\in G$ and receives $x*y$. We study randomized adaptive two-sided property testers for deciding whether $(G,*)$ ... more >>>

I give a short proof that the border determinantal complexity of F_n = x_1^n + ... + x_n^n over C is at least (n-1)^2/(4e), and at least (n-1)^2/(2e) in the symmetric model. The same argument shows that the border determinantal complexity of x_1^d + ... + x_N^d is Theta(Nd) for ... more >>>