Let $\mathbb{F}_q$ be a finite field and $f(x) \in \mathbb{F}_q(x)$ be a rational function over $\mathbb{F}_q$. The decision problem {\bf PermFunction} consists of deciding whether $f(x)$ induces a permutation on the elements of $\mathbb{F}_q$. That is, we want to decide whether the corresponding map $f : \mathbb{F}_q \mapsto \mathbb{F}_q$ defined ... more >>>