The sum of minimum and maximum number of final states for a Deterministic…
2023
The sum of minimum and maximum number of final states for a Deterministic Finite Automata (DFA) having 'P' state is equal to :
- A.
p
- B.
p - 1
- C.
p + 1
- D.
p + 2
Attempted by 473 students.
Show answer & explanation
Correct answer: A
Answer: p
Minimum and Maximum Values: Following the formal definition:
Minimum: The minimum number of final states is 0. This occurs when a DFA recognizes the "Empty Language" (∅), where no input string is ever accepted.
Maximum: The maximum number of final states is p. This occurs when every state in the DFA is an accepting state, recognizing all strings in the language Σ∗.
The Resulting Sum: When you add the formal minimum (0) and the maximum (p), the sum is 0+p=p. This logic is universal across theoretical computer science unless a specific constraint (like "the language must be non-empty") is explicitly mentioned.