For the above specified passage, which of the following is DFA for the language represented/accepeted by machine?

The correct answer is : Option 3

Key Points

Option 1: This DFA starts with state 1 looping on a and b. Then from 1 --a--> 2, 2 --b--> 3, and 3 --b--> 4. After reaching state 4, it loops on a and b and accepts. Looks promising, but lacks rejection for incorrect sequences like “aba”. It accepts too many patterns and has no trap state to reject wrong combinations. Incorrect.

Option 2: This DFA takes a → b → a → b → final. This structure doesn’t track “abb” correctly; it adds unnecessary transitions and doesn’t form the required substring properly. Incorrect.

Option 3: This DFA clearly implements the pattern detection:

• q1 --a--> q2
• q2 --b--> q3
• q3 --b--> q4 (final)
• q4 is the accepting state, loops on all inputs (a, b)
• Other transitions (like wrong 'a' or 'b') push to dead states