Which ONE of the following languages is accepted by a deterministic pushdown automaton?

A Deterministic Pushdown Automaton (DPDA) accepts the class of Deterministic Context-Free Languages (DCFLs).

• Regular languages: Every regular language can be accepted by a Deterministic Finite Automaton (DFA). Since any DFA can be simulated by a DPDA (by simply ignoring the stack), every regular language is deterministic context-free and can be accepted by a DPDA. Hence, (A) is correct.

• Context-free languages / NPDAs: DPDAs are strictly less powerful than Non-Deterministic Pushdown Automata (NPDAs). There exist non-deterministic context-free languages (e.g., the language of even-length palindromes $\{ww^R \mid w \in \{a, b\}^*\}$) that cannot be recognized by any DPDA. Thus, (B) and (C) are false.

• Decidable languages: The class of decidable languages contains context-sensitive and other non-context-free languages (e.g., $\{a^n b^n c^n \mid n \ge 0\}$) which cannot be accepted by any pushdown automaton. Thus, (D) is false.