Question: ( 1 ) Give a string $ omega$ $ in$ $ sum _ { 4 } ^ { * } $ satisfying

(1) Give a string $\omega$ $\in$ $\sum_{4}^{*}$ satisfying $\psi_{2}$(11001110100)= $\psi_{4}$($\omega$).
(2) Give a string $\omega$ $\in$ $\sum_{2}^{*}$ satisfying $\psi_{2}$($\omega$)= $\psi_{4}$(130321).
(3) Draw the minimum DFA that accepts the language { $\omega$ $\in$ $\sum_{2}^{*}$ | $\psi_{2}$($\omega$) is a multiple of 3}.
(4) Draw the minimum DFA that accepts the language { $\omega$ $\in$ $\sum_{4}^{*}$ | $\psi_{4}$($\omega$) is a multiple of 3}.

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