Question

Show that the language L = {an : n ≥ 0, n != 3} is regular.

Comments

Draw the DFA for L = {a^n | n>=0, n = 3}, It will have 5 states with 4^th state as the Final state. Now take L’(Final state → Non Final state and Non Final state → Final State) to get the Language you have mentioned i.e L’ = {a^n | n>=0,n!=3}.

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is it $a^n$ or $an?$

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I guess it’s a^n only. Otherwise if its an then Alphabet set Sigma would be infinite ={ a, 0, 1, 2, 4,…….}