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2. (15 points) Design a minimum DFA for the following language (10 points), and please briefly describe the strings corresponding to each state (5 points). Functions na(x) and ) are the numbers of as and bs in string x, respectively L(x over (a, b) | (2*a)bx) mod 3 0) For example, the following strings are all members of L: e, ab, aab, bbb, babaFigure 2: minimum DFA 2 Question 2 For b, 1 mod 3- 1, hence we connect so to s1 for b For bb, 2 mod 3 -2, hence we connect si to s2 for b For bbb,3 mod 3 -0, hence we connect s2 to so for b For a, 2*1 mod 32, hence we connect so to s2 for a For aa, 2*2 mod 3-1, hence we connect s2 to s1 for a For aaa,3*2 mod 3 0, hence we connect s1 to so for a For ab, 1*2+1 mod 3-0, it is simplified For abb, 1*2+2 mod 3-1, it is simplified For abbb, 1*2+3 mod 3-2, it is simplified For abbbb,1*2+4 mod 3-0, it is simplified For aab, 2*2+1 mod 3 -2 ,it is simplified For aabb, 2*2+2 mod 3-0,it is simplified For the featuers of state For so, 2na(x) + nb(z) mod 3-0 For s1, 2na(x) +nb(x) mod 3-1 For s2, 2na(z) +nb(x) mod 3-2

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