Answer

Correct Option: (ii) universal Turing machine

Explanation

Universal Turing Machine $U$: A TM that takes as input encoding of any TM $M$ and input $w$: $U(\langle M, w\rangle) = M(w)$.

• Can simulate any other TM (stored-program concept).
• Basis for von Neumann architecture, stored-program computers.
• Exists by Church-Turing thesis; constructed by Turing (1936).
• Leads to undecidability of halting problem.

Other options:

• Nested TM — not standard.
• Counter machine — weaker (but Turing-equivalent with 2 counters).

Final Answer

Universal TM → Option (ii).