Consider the following problem: For finite automata it is of course decidable to check if the recognized language is finite, but this obviously not the case for TMs but I wonder if it is possible to decide whether $L(M)$ is finite if you already know (e.g. by some oracle) that $L(M)$ is regular.
I am thinking of an answer where one might construct an FA $\mathcal{A}$ from a TM $M$ with $L(\mathcal{A}) = L(M)$. Is there any way?
Best, Niklas