For each of the following NFAs, use Algorithm $5\mathrm{.}6\mathrm{.}3$ to construct the state diagram of an equivalent DFA.

a$)$

b$)$

c$)$

d$)$

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 $n{Q}^{\text{'}}$ 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 $Y!in{Q}^{\text{'}}$inx, 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$\}$