Completeness problem for dcfls is decidable.
It depends on emptiness problem.
Whether given DCFL is sigma*? is decidable problem.
Step 1) For given dcfl L, design DPDA D.
Step 2) Modify dpda to accept complement of L by interchanging finals and nonfinals.
Step 3) If modified DPDA accepts empty language, then given dpda D accepts sigma*. Otherwise not.
So completeness problem for dcfls is decidable.
Thanks,
Mallesham Devasane