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{"ops":[{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Question 2:"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Create a DFA D to recognize all strings of 0\u2019s and 1\u2019s representing binary numbers divisible by three. "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Assume the binary string 0 represents the number 0, 1 represents 1,  00 represents 0, 01 represents 1, 10 represents 2, 11 represents 3, and so on. Also, assume the empty string represents the number 0. "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Also, assume that D has the following properties:"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"A finite set of states Q = {A, B, C}"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"The input alphabet Z = {0, 1}"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Start state A"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"The set of final states F = {A}"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"State \u2018A\u2019 represent all prefixes of binary strings that are Congruent to 0 mod 3, State \u2018B\u2019  all prefixes congruent to 1 mod 3,  and State \u2018C\u2019  all prefixes congruent to 2 mod 3. "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"a) Draw the DFA D  (the state diagram for DFA D)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"b) Define the transition table for DFA D"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"c) Show the  DFA D processing the string 1001"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"d) Prove that the language  defined by DFA D is the  set  of all binary strings representing  integers divisible by three."},{"insert":"\n"}]}

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