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

The correct option is Any regular language.

To understand why this is correct, we can analyze the relationships between different classes of automata and the languages they accept.

A Deterministic Pushdown Automaton (DPDA) is a computational model that is similar to a Deterministic Finite Automaton (DFA) but has the added capability of using a single stack memory. The class of languages accepted by DPDAs is known as the Deterministic Context-Free Languages (DCFLs).

Any regular language can be recognized by a standard DFA. Since a DFA is simply a DPDA that does not make use of its stack (or leaves the stack stack-pointer unchanged), any language that can be accepted by a DFA can also be accepted by a DPDA. Thus, the set of regular languages is a strict subset of the set of deterministic context-free languages. Therefore, any regular language is accepted by a deterministic pushdown automaton.

Let's examine why the other options are incorrect:
- Any context-free language: The class of Context-Free Languages (CFLs) is larger than the class of DCFLs. Some context-free languages are inherently non-deterministic and cannot be accepted by any deterministic PDA (for example, the language of even palindromes).
- Any language accepted by a non-deterministic pushdown automaton: A non-deterministic pushdown automaton (NPDA) accepts the entire class of Context-Free Languages. Because DPDAs cannot accept all CFLs, they cannot accept every language that an NPDA can accept.
- Any decidable language: Decidable languages include languages that are not context-free, such as:
$a^n{b}^n{c}^n$
These require more powerful machines, like Turing machines, and cannot be accepted by a DPDA.