Solution

The correct answer is: Option 1) P

Key Points

Given: A Deterministic Finite Automaton (DFA) with P states.

Goal: Find the sum of the minimum and maximum number of final states the DFA can have.

1. Minimum Number of Final States:

• A DFA is allowed to have zero final states.
• This would mean the DFA rejects all strings regardless of input.

✅ Minimum = 0

2. Maximum Number of Final States:

• Since there are P states, we can make all of them final states.
• This would result in the DFA accepting many possible strings.

✅ Maximum = P

Sum of Minimum and Maximum = 0 + P = P

✅ Final Answer: Option 1) P