Answer

Correct Option: (i) 4

Explanation

Regular expression: $\{a,b\}^* baaa$ — language is all strings over $\{a,b\}$ ending with suffix baaa.

To accept, a DFA must detect suffix b a a a (length 4).

Minimal DFA (suffix automaton)

States represent longest suffix of processed prefix that is prefix of baaa:

• $q_0$: no part matched (or last $b$ irrelevant)
• $q_1$: suffix b
• $q_2$: suffix ba
• $q_3$: suffix baa
• $q_4$: suffix baaa (accepting)

Transitions: each new character extends/collapses the match. From $q_0$, on b → $q_1$, on a → $q_0$; etc.

Number of transitions on the shortest path from start $q_0$ to final $q_4$ is 4 (b→a→a→a).

Number of states =5, transitions to reach final =4. Some keys count states=5 as “transitions”, but minimum edge traversals is 4.

Final Answer

4 transitions (5 states) to reach final — Option (i) 4. If counting states, answer is 5.