theory of computation

Question

Find dfa's for the following languages on Σ = {a,b}.

L= {w: n_a(w) mod 3 >n_b(w) mod 3}.

L= {w :(n_a(w) – n_b(w)) mod 3 > 0}.

Answer 1

DFA for n_a(w) mod 3 

DFA for n_b(w) mod 3

DFA for n_a(w) mod 3 >n_b(w) mod 3

Final states would be {10, 20, 21}

For second one, (n_a(w) – n_b(w)) mod 3 > 0

I think, final states should be {10, 20, 21}

Comments

thanks ...but 22 is not a final state ....

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Oh. yes, coz it is giving 0 and mod greater than 0 needed

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very well explained broo thanks

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i think the l2 language is not same as l1 https://gateoverflow.in/123485/theoryof-computation 

check tis out