Consider L $=\{$abwba : w in $\backslash$Sigma

$$ but does not contain the substring ba$\}$ over $\backslash$Sigma $=\{$a$,$ b$,$ c$,$ d$\}.$

$1.$ Show that L is a regular language by drawing a DFA for it$,$ with the DFA having

as few states as you can.

$2.$ Draw an NFA for L with as few states as you can.

$3.$ Convert the NFA to a GNFA.

$4.$ Convert the GNFA to an RE $($Regular Expression$)$ using the procedure discussed

in class. Show the steps. You may, but are not required to$,$ shorten intermediate

REs using identities like R$=$ and $\backslash$epsi R $=$ R and R $\backslash$cup $=$ R to reduce expression

swell.