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Draw the state diagram for a DFA over the alphabet{0,1}that recognizes the following language: {w=w1w2...wk^ | (w1w2+w3+(1)^{k1}wk) mod 4 = 0 for all k0 and

Draw the state diagram for a DFA over the alphabet{0,1}that recognizes the following language:

{w=w1w2...wk^ | (w1w2+w3+(1)^{k1}wk) mod 4 = 0 for all k0 and each wi{0,1}}(please also, if possible, explain the role of each state in your DFA. If your DFA is too compli-cated, then just explain how you designed it.)

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