Step 1: Recall what a deterministic pushdown automaton is.
A deterministic pushdown automaton (DPDA) is a pushdown automaton in which the next move is uniquely determined.
For any given state, input symbol, and top stack symbol, there is at most one valid transition.
Unlike a nondeterministic PDA, a DPDA cannot branch into multiple computational paths.
Step 2: Identify the class of languages recognized by DPDAs.
DPDAs recognize a special subclass of context-free languages known as deterministic context-free languages (DCFLs).
Although this class is smaller than the class of all context-free languages, it still includes all regular languages.
Step 3: Understand the hierarchy of language classes.
The inclusion relationship among these classes is:
\[ \text{Regular Languages} \subseteq \text{Deterministic CFLs} \subseteq \text{Context-Free Languages} \]
Step 4: Evaluate the given options.
(A) Any regular language: This is correct. A DPDA can simulate a finite automaton and may even ignore its stack entirely.
(B) Any context-free language: This is incorrect, since some CFLs require nondeterminism and cannot be handled by a DPDA.
(C) Any language accepted by an NPDA: Incorrect, because nondeterministic PDAs are strictly more powerful than deterministic ones.
(D) Any decidable language: Incorrect, as many decidable languages lie outside the context-free family.
Step 5: Final conclusion.
A deterministic pushdown automaton can accept:
\[ \boxed{\text{Any regular language}} \]