Unique decipherability of infinite regular language
McCloskey gave such an algorithm in his paper An $O(n^2)$ Time Algorithm for Deciding
Whether a Regular Language is a Code. Given an NFA on $n$ states, his algorithm runs in time $O(n^2)$. Since a regular expression of length $n$ can be converted to an NFA with $O(n)$ states in linear time, McCloskey's algorithms runs in quadratic time even when given a regular expression as an input.