In Knuth's original paper on $LR(k)$ grammars, he proved that the decision problem "Given a CFG $G$, is there a $k$ such that $G$ is an $LR(k)$ grammar?" is undecidable.
Is there a similar result showing that it is undecidable whether a given CFG is an $LL(k)$ grammar for some choice of $k$? Or is this problem known to be decidable?