Let's consider two context-free grammars $G_1$ and $G_2$ and ask the following question: Is $L(G_1) = L(G_2)$, that is, are the two grammars equivalent?
In general, this problem is undecidable. However, if both $G_1$ and $G_2$ are left-linear (or right-linear) grammars, then the problem is decidable, because both grammars describe regular languages.
My question is whether or not the same problem is decidable when both grammars are linear. Also, if anybody can point to relevant literature, that will be highly appreciated!