Greibach famously defined a language $H$, the so-called nondeterministic version of $D_2$, such that any CFL is an inverse morphic image of $H$.  Does there exist a similar statement with DCFL, possibly with some restriction on the morphisms allowed?(See, e.g., M. Autebert, J. Berstel, and L. Boasson. Context-free languages andpushdown automata. In R. Rozenberg and A. Salomaa, editors,Handbook of Formal Languages, volume I, chapter 3. Springer Verlag, 1997.)
Does there exist a hardest DCFL?
fl.formal languages;open problem;context free;nondeterminism;hard instances