A Note on Limited Pushdown Alphabets in Stateless Deterministic Pushdown Automata

Abstract: 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.