Which of the following represented the minimum state DFA for the above specified passage?

The correct answer is: Option 1

Key Points

To detect “abb”, we need at least 4 states:

1. q0 — Start state
2. q1 — After seeing 'a'
3. q2 — After seeing 'ab'
4. q3 — After seeing 'abb' → Accepting

We also need a dead state to trap wrong transitions. So the **minimum** DFA needs at least 5 states.

Option 1: This DFA uses 5 states correctly and has transitions:

• q1 → q2 (on a)
• q2 → q3 (on b)
• q3 → q4 (on b) → final
• Final state loops on a, b

Option 2: Incorrect transitions. Accepts some but not all “abb” variants. Incorrect

Option 3: Uses 6 states, which is not optimal/minimal. Incorrect