Consider the following DFA that generates set of Σ = {a, b, c} strings over

Now identify that which of the followings is the best description of the language for the above DFA

1. AL = (a* + b* + c*)⁺
2. BL = (a + b + c)* (abc)⁺ (a + b + c)*
3. CL = { strings starting with a, b or c but ending with c }
4. DL = { strings having an even count (including 0) of the substring 'abc' }

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: D. L = { strings having an even count (including 0) of the substring 'abc' }

Explanation

The start state q0 is the only accepting state. Reading a, b, c in sequence (q0 → q1 → q2 → q3) moves to the non-accepting half of the machine, and a second 'abc' (q3 → q4 → q5 → q0) returns to q0. Other symbols fall back without completing the pattern, so the machine accepts strings with an even number of 'abc' occurrences.