Question
Download Solution PDFComprehension
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)
Detailed Solution
Download Solution PDFThe correct answer is: Option 1
Key Points
To detect “abb”, we need at least 4 states:
- q0 — Start state
- q1 — After seeing 'a'
- q2 — After seeing 'ab'
- 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