Finite State Machines

$($a$)$ Using the subset algorithm, convert the following NFA to a DFA, and fill in the

blanks appropriately matching the DFA provided with the right nodes and transitions.

Only the blanks will be graded. NFA:

ura:

S$1$:

S$5$:

E$4$:

E$4$:

$4$:

S$2$:

E$1$:

E$5$:

S$3$:

E$2$:

E$6$:

S$4$:

E$3$:

E$7$:

$($b$)$ Which of the following are the final states? Select all that apply.$()(5$points$)$

A$.S1$

B$.$ S$2$

C$.$ S$3$

D$.$ S$4$

E$.$S$5$

F$.$None

$($c$)$ Write a regex to describe the language of the above NFA.$(5$ points$)$