5 problems

Let $H\unlhd F_k$ be a normal hidden subgroup of a free group $F_k$, possibly of infinite index, and encode elements of $F_k$ as canonical compressed words. Infinite-index free-gro…

Let $H\unlhd F_k$ be a normal hidden subgroup of finite index, let $G=F_k/H$ be the resulting finite group, and assume that $|G|$ is bounded by a quantity exponential in a paramete…

Let $H\subseteq F_k$ be a hidden subgroup, and suppose the question is whether $H$ is a non-trivial element of length $\operatorname{poly}(n)$, while the index $[F_k:H]$ can have e…

Let $G$ be an infinite group, and consider the Hidden Subgroup Problem (HSP) for $G$, namely the problem of determining a hidden subgroup from oracle access to a function that is c…

Let $\mathbb{A}$ be a finite algebra, and let a cube term be a term operation $t(x_1,\dots,x_n)$ such that, for every $i\in[n]$, there is a choice of $u_1,\dots,u_n\in\{x,y\}$ with…