Let the word be “automata”. The total number of states required to recognize…

Solution

To recognize a fixed word of length n using a DFA, we need:

• One start state

• One state for each character matched so far

• One final (accepting) state after the complete word is recognized

The word "automata" has 8 characters:

a u t o m a t a

Therefore,

Number of states = Length of word + 1

= 8 + 1

= 9 states

Hence, if we count only the states required to recognize the word, the DFA requires 9 states.

Note: If a complete DFA is constructed, an additional dead (trap) state is required to handle all invalid transitions. In that case, the total number of states would be 10. However, in such questions, the dead state is typically not counted unless explicitly mentioned. Therefore, the expected answer is 9 states.

Correct Answer: Option A (9 states).