doubt

Question

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And to the person whose downvoting, if you have a counter argument please do share your thoughts rather than just downvoting:-D :-D...

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we can draw DFA for L1 having regular expression R = (aa)* (bb)* + a(aa)* b(bb)*
but for L2 need infinite comparison & counting so it will not be regular

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Cool man thanks!

Answer 1

i)m+n should be even and we know even + even =even  and odd+odd=even

So we can draw a DFA having even no of a's and even no of b's or with odd no of a's and odd no of b's.

L1=(aa)*(bb)* + a(aa)*b(bb)*

ii)But for L2 it is given m-n=4 which means we need to do  comparison and count no of a's and b's  which is not possible with DFA's because it has finite memory.