Test-Series

Question

Consider the following language over $\sum$ = {0, 1}

L = {w | w $\epsilon \sum$ * and |w| is divisible by 2 and not by 4}

How many sates will min-DFA accepting L will have?

Comments

@Kabir5454

no bro 

4 is given.

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Correct.

Length of strings accepted are {2,6,10,14,18,....4n-2,......}

So if we notice carefully every length of the string gives us remainder of 2 while divide by 4.

So according to myhill nerode theorem it has 4 equivalent state where the state where lenght mod 4=2 will be the final state.

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@Kabir5454 Yes, that’s the correct reason.

Thanks.

Answer 1

only  4 state