Problem $2$

Add a new state, and merge the two NFAs to share the same "start" state, like the right figure that merges two regular expressions a and $a**bb**.$ Then, convert your NFA to DFA using the

algorithm discussed in class. Draw your transition table or DFA diagram, and show your work to get full points.

In your transition table, if you cannot define a transition state since it becomes an empty set $($a dead state$),$ mark it as $"-".$ In your DFA diagram, you do not need to draw dead states.

After determining DFA, mark the final states using double circles, and identify their accepting tokens.

Problem $3$

Minimize your DFA by performing the following steps:

$1.$ Add a dead state $$ into your DFA $($you can omit this step of adding the dead state$)$;

$2.$ Minimize its states using the Moore's algorithm discussed in class;

$3.$ Delete the dead state $$ from your minimized DFA;

$4.$ Draw its final minimized diagram.

You can minimize DFA using Moore's algorithm without explicitly introducing dead states $($in step $1).$

After determining minimized DFA, mark the final states using double circles, and identify their corresponding accepting tokens.