Deterministic Pda and Simple Languages 1 1

A context-free language is said to be simple if it is accepted by a single-state deterministic pushdown automaton with empty Stack acceptance. This paper proves that it is decidable whether a deterministic pushdown automaton (dpda) accepts a simple language. For this purpose, we prove that it is decidable whether a real-time dpda with empty stack acceptance accepts a simple language. To prove this, we present two conditions called nonsingularity and separability conditions and show that for a real-time dpda M with empty stack acceptance, (i) the language accepted by M is simple if and only if M satisfies the two conditions, and (ii) it is decidable whether M satisfies the two conditions.