1. (Extra credit: 16 points) Given the following NFA over the alphabet {a,b}, to transform the given NFA to a DFA, first construct -closures of all the states of the given NFA. Fill out the blanks for state 1 and state 3 . (1 point) (0)=(1)=(2)={2,3}(3)={3} Next to get the states of the DFA, we construct a tree as follows. Fill out the blanks in the tree. ( 3 points) The distinct nodes of the above tree are listed below. Fill out the missing nodes. (1 point) These are the states of the DFA to be constructed and we have the following transition table for the DFA. Fill out the missing entries in the table. (4 points) Now replace the states in the first column of the above table top down by 0,1,2, and 3 in that order, the transition table of the DFA becomes of the following form. Fill out the missing entries in the table. (2.5 points) Hence, a DFA can be constructed as follows. Fill out the missing labels in the DFA. ( 2.5 points) Expression of the given NFA is (1 point) Expression of the resulting DFA is