Two technical details:

1. To make definition work, not only should "delta" the transition function, be a function (as opposed to a relation, the case for pdas), but we must make sure that there is either an epsilon-transition or a normal transition, but not both
2. We need endmarkers, both for the input string and for the stack to make dpdas work.

To make the theorem "dcfl closed under complement" work, must eliminate infinite loops on epsilon-transitions.

Closure properties of cfls and dcfls