  Recently, an infinite hierarchy of languages accepted by stateless
deterministic pushdown automata has been established based on the number of
pushdown symbols. However, the witness language for the n-th level of the
hierarchy is over an input alphabet with 2(n-1) elements. In this paper, we
improve this result by showing that a binary alphabet is sufficient to
establish this hierarchy. As a consequence of our construction, we solve the
open problem formulated by Meduna et al. Then we extend these results to
m-state realtime deterministic pushdown automata, for all m at least 1. The
existence of such a hierarchy for m-state deterministic pushdown automata is
left open.

Formal Languages and Automata Theory