The sum of minimum and maximum number of final states for a Deterministic Finite Automata (DFA) having ‘P’ state is equal to :

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UGC NET Computer Science (Paper 2) 07 Dec 2023 Official Paper
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  1. P
  2. P - 1
  3. P + 1
  4. P + 2

Answer (Detailed Solution Below)

Option 3 : P + 1
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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50 Questions 100 Marks 60 Mins

Detailed Solution

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The correct answer is P + 1

EXPLANATION:

  • Minimum Number of Final States (min):
    • The minimum number of final states for a DFA can be 1.
    • Therefore, we have min = 1.
  • Maximum Number of Final States (Max):
    • The maximum number of final states for a DFA can be n.
    • In this case, every state is a final state.
    • Therefore, Max = P.
  • Sum of Minimum and Maximum Number of Final States:
    • The sum of m and M is equal to 1 + n, which simplifies to n.
    • Therefore, the answer is option A, n + 1.
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