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

Answer: Any regular language.

Reasoning:

• Deterministic pushdown automata (DPDA) recognize deterministic context-free languages (DCFLs).

• Every regular language is deterministic context-free because a DPDA can simulate a deterministic finite automaton by not using the stack (or using it in a trivial deterministic way). Thus every regular language is accepted by some DPDA.

• Not all context-free languages are deterministic context-free. For example, the language of palindromes over {a,b} is context-free but cannot be recognized by any DPDA, so the statement that every context-free language is accepted by a DPDA is false.

• Languages accepted by nondeterministic pushdown automata are exactly the context-free languages; since some of these are not deterministic, not every language an NPDA accepts can be accepted by a DPDA.

• Decidable languages form a much larger class that includes languages which are not context-free (for example, {a^n b^n c^n | n ≥ 0} is decidable but not context-free), so they are not all accepted by DPDAs.

Therefore, among the given choices, the only class guaranteed to be accepted by a deterministic pushdown automaton is the class of regular languages.