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Problem $1$: RE $->$ NFA$-$& $($From week$5$a$)[6$ pts per machine $=36$ points$]$

Give NFA$-$ for the following REs.

Show component machines first

and then show all steps of connecting these machines using the methods

described in week$6$a notes.

Hand$-$drawing is $0K($just insert into this file$).[6$ pts per machine$]$

Do not use any simplification. Having many $-$moves is what we want.

The following is for $x(z|{)}^{{?}^{{?}^{?}}**}$

No state numbers are needed for components.

M$1$ for $x$:$**??*$

M$2$ for z:

M$3$ for $$ by connecting M$1\text{'}$s with an arrow :

Start combining them now $($show all states$).$

M$4$ for $(z|)$ combining M$2$ and M$3$ :

M$5$ for $(z|{)}^{{?}^{{?}^{?}}**}$ modifying M$4$ : $,??3$

The whole thing for $x(z|{)}^{{?}^{{?}^{?}}**}$: :$??{?}^{**}$

HINT: Put M$1$ in front of M$5$ connected with a blank arrow and then give state numbers finally

$($make sure state numbers are unique$)$