Does anyone know whether the following decision problem is decidable:
Given a context-free language $L$, is $L$ regular?
Here $L$ can be expressed, e.g., using a context-free grammar. Does anyone know an algorithm that takes as input a context-free grammar $G$ and outputs an equivalent regular grammar $G'$, i.e. $L(G) = L(G')$, if $L(G)$ is regular?