$(2$ point$)$ Convert the regular expression $a(abb{)}^{*}b$ into a NFA.

Determine regular expressions for this automaton:

$(1$ point$)$ Use $L(M)=(r_1^{*}{r}_2(r_4{r}_3{r}_1^{*}{r}_2{)}^{*}),$ slide $7-10,$ to get a regular expression.

$(3$ points$)$ For this automaton use formula $E_{i,j}^{k+1}=E_{i,j}^k{E}_{i,k+1}^k(E_{k+1,k+1}^k{)}^{*}{E}_{k+1,j}^k,$ the

resulting regular expression $E_{1,2}^2$ will be very long, use a table like this to keep track of

intermediate results:

$(1$ point$)$ Use JFLAP to determine a reg. ex$.$

$(1$ bonus point$)$ Show that $E_{1,2}^2$ is identical to the

reg. exp. $L(M)=(r_1^{*}{r}_2(r_4{r}_3{r}_1^{*}{r}_2{)}^{*}),$ slide

$7-10,$ derived above. You can use $(a{)}^{*}=a^{*},$

$(b{a}^{*}b)=a^{*}b$ and other ways to simplify.

I need help with EVERY part of this except for the $3$ point question, and detailed explanation as I am really struggling to grasp how to asnwer these questions and how to work with JFLAP, at least with how to get everything to come together and what its supposed to look like because every regular expression I come up with look completely messy and unnatural and I have no way of confirming if what im doing is correct or in the correct way.