Problem $3.(15$ points$)$ For any string $=!"$& $,$ the reverse of $,$ written $\text{'},$ is the

string $$ in reverse order, $$& $"!.$ For any language $,$ let $\text{'}=\{\text{'}|$ in $\}.$

Show that if $$ is regular, so is $\text{'}.$ Specifically, describe the steps to generate a DFA for $\text{'}$

starting with a given DFA for $.$

$($Hint: How do we modify a DFA to run backwards? Does that result in a DFA?$)$