For a Non-deterministic Finite Automaton (NDFA) with \( N \) number of states, the equivalent Deterministic Finite Automaton (DFA) has \( D \) number of states. Then, possible number of states in DFA can be defined as:
Show Hint
- \( N \times 2 \)
- \( N + 2 \)
- \( 2^N \)
- \( N \times D \)
The Correct Option is C
Solution and Explanation
Step 1: Understanding NDFA to DFA conversion.
In the conversion from a Non-deterministic Finite Automaton (NDFA) to a Deterministic Finite Automaton (DFA), the number of states in the DFA is determined by the power set of the states of the NDFA. For an NDFA with \( N \) states, the DFA may have up to \( 2^N \) states because each state of the DFA corresponds to a subset of states of the NDFA.
Step 2: Conclusion.
Therefore, the possible number of states in the equivalent DFA is \( 2^N \), making the correct answer (3).
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