Which one of the following is TRUE?

Let us evaluate the options:

• (A) $L = \{a^n b^n \mid n \ge 0\}$ is a classic deterministic context-free language that is not regular, as it requires unbounded memory to match the number of $a$'s and $b$'s.

• (B) $L = \{a^n \mid n \text{ is prime}\}$ is not regular since the sequence of prime numbers cannot be tracked by any finite automaton.

• (C) $L = \{w \mid w \text{ has } 3k + 1\ b\text{'s for some } k \in \mathbb{N} \text{ with } \Sigma = \{a, b\}\}$ represents strings where the number of $b$'s satisfies $|w|_b \equiv 1 \pmod 3$. This can be easily recognized by a 3-state Deterministic Finite Automaton (DFA) that tracks $|w|_b \pmod 3$. Therefore, this language is regular.

• (D) $L = \{ww \mid w \in \Sigma^* \text{ with } \Sigma = \{0, 1\}\}$ is not regular (nor context-free) as it requires matching two arbitrary-length copies of $w$.

Thus, only (C) is TRUE.