Comprehension

A machine is represented by states Q, input alphabet Σ, transition function δ. Initial state qo and final state F. The machine accepts all the strings over Σ = {a,b}, which starts and ended with any combination of all alphabet and abb works/lies in all the strings to be accepted 

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

Answer (Detailed Solution Below)

Option 1 :

Detailed Solution

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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

This is a proper minimal DFA. Correct ✔

 

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

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

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