Q$2.$ NO ChatGPT please or AI$,$ if possible with pen and pencil, if formatting is not clear I will reject the answer

Consider the following state transition diagram over $=\{0,1\}$ :

Using the method described in class and in the textbook $($Section $9\mathrm{.}2)$ convert the diagram

into an equivalent regular expression. Include all the intermediate steps in your answer.

Are the languages $L_1$ and $L_2$ below over the alphabet $=\{a,b,c\}$ regular or non$-$regular?

Justify your answer carefully.

$($a$)L_2=\{a^{2i}{b}^j{c}^i$:$i0,j>2\}$

$($b$)L_1=\{a^i{b}^{2j+1}$:$i,j0\}\{a^{2k+1}{b}^{2n}{c}^{2p}$:$k,n,p0\}$

Make sure you review the submission guidelines posted on the course's Web site before handing

in your answers.