Let $M$ be the NFA$-$

a$)$ Compute $-$closure $(q_i)$ for $i=0,1,2,3.$

b$)$ Give the input transition function $t$ for $M.$

c$)$ Use Algorithm $5\mathrm{.}6\mathrm{.}3$ to construct a state diagram of a DFA that is equivalent to M$.$

Algorithm $5\mathrm{.}6\mathrm{.}3$

Construction of DM$,$ a DFA Equivalent to NFA$-$ M

input: an NFA $-M=(Q,,,q_0,(F))$

input transition function $t$ of $M$

initialize $Q^{\text{'}}$ to $-$closure $(q_0)$

repeat

$2\mathrm{.}1.$ if there is a node $xin{Q}^{\text{'}}$ and a symbol ain$$ with no arc leaving $x$ labeled $a,$ then

$2\mathrm{.}1\mathrm{.}1.$ let $Y=u_{q_i\text{i}\text{n}\text{x}}t(q_i,a)$

$2\mathrm{.}1\mathrm{.}2.$ if $Y!in{Q}^{\text{'}},$ then set $Q^{\text{'}}$:$=Q^{\text{'}}\{Y\}$

$2\mathrm{.}1\mathrm{.}3.$ add an arc from $x$ to $Y$ labeled $a$

else done :$=$ true

until done

the set of accepting states of $DM$ is $|)$:$\}$ contains an element $\{$:$q_i$inF$\}$