Answer

Correct Option: (ii) Turing Machine

Explanation

A language $L$ is called Recursively Enumerable (RE) iff there exists a Turing Machine $M$ such that $L = L(M)$, i.e., $M$ halts and accepts exactly the strings in $L$. On strings not in $L$, $M$ may either reject or loop forever. This is the most general language class in the Chomsky hierarchy (Type-0).

Why other options are incorrect

• (i) DFA : Accepts Regular languages (Type-3), strictly smaller than RE.
• (iii) PDA : Accepts Context-Free Languages (Type-2), also properly contained in RE.
• (iv) Linear Bounded Automaton (LBA) : Accepts Context-Sensitive Languages (Type-1), also a proper subset of RE.

Hierarchy recall

$$\text{REG} \subset \text{CFL} \subset \text{CSL} \subset \text{RE} \subset \text{ALL}$$

• REG → DFA
• CFL → PDA
• CSL → LBA
• RE → Turing Machine
• Recursive → Decidable TM (always halts)

Final Answer

Hence, Recursively Enumerable Languages are exactly those accepted by Turing Machines. Correct answer is (ii) Turing Machine.