A real-time strictness test for deterministic pushdown automata

A context-free language is said to be real-time strict if it is accepted by a real-time deterministic pushdown automaton with empty stack acceptance. This paper proves that there exists an effective procedure for deciding whether the language accepted by a deterministic pushdown automaton (dpda) is real-time strict. The result implies the following: For any subclass ℰ of real-time dpda's with empty stack acceptance, the problem for deciding whether a dpda is equivalent to some machine in ℰ reduces to that for deciding whether a real-time dpda with empty stack acceptance is equivalent to some machine in ℰ.