Answer

Correct Option: (i) Finite automaton with a stack

Explanation

PDA definition: $P = (Q,\Sigma,\Gamma,\delta,q_0,Z_0,F)$

• Essentially a finite automaton (finite control) augmented with a stack (LIFO memory).
• Stack provides unbounded memory but restricted access (push/pop at top only).
• Enables recognition of CFLs: e.g., $\{a^n b^n\}$ by pushing $a$'s, popping for $b$'s.

Options:

• (ii) TM with stack → equivalent to TM (stack is not needed)
• (iii) FA with queue → queue automaton = TM-powerful
• PDA = FA + stack.

Final Answer

PDA = FA + stack → Option (i).