Design a DFA that accepts the string given by L = { w has number of 'a' divisible by 3 and number of 'b' divisible by 2 over the alphabet {a,b} }
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Miraj50
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Suraj Oberai
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1What have you tried, and where are you stuck with your attempted solution? – Welbog Jan 17 '19 at 19:40
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@Welbog i am not getting any idea about it , could u just show me the transition states of the given dfa – Suraj Oberai Jan 19 '19 at 11:33
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Realize that we should have 3 * 2 = 6 states in the DFA. Why? Because one has 3 choices for the number of a's (0 or 1 or 2) [think in terms of remainders] and 2 choices for number of b's (0 or 1 similarly).
Let us name the states axby which means I have found x number of a's and y number of b's till now. For example, if we are in a2b0 and we encounter an a, then we go to a0b0 (hope you see why?). Similarly a1b1 ---b---> a1b0 and a1b1 ---a---> a2b1.
Needless to say a0b0 is the accepting state.
Now, all you have to do is draw the states and keep joining them. I have drawn them on a paper here.
Miraj50
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