Under which of the following operation, NFA is not closed?

Solution

The class of languages accepted by Non-deterministic Finite Automata (NFA) is closed under several fundamental operations. Let's analyze each option:

• Negation (Complement): NFA is closed under complementation. Although direct construction is difficult, we can convert the NFA to a Deterministic Finite Automaton (DFA), complement the DFA, and convert it back to an NFA.

• Kleene Closure (Star): NFA is closed under the Kleene star operation. We can construct a new NFA by adding epsilon transitions from the new start state to the old start state and from old accepting states back to the start state.

• Concatenation: NFA is closed under concatenation. We can create a new NFA by adding epsilon transitions from the accepting states of the first NFA to the start state of the second NFA.

Since NFA is closed under negation, Kleene closure, and concatenation, there is no operation among the first three options under which it is not closed. Therefore, the correct choice is 'None of the above'.