Homework $4$ Points evenly distributed $1.$ Convert the following NFA to DFA $2.$ Convert the following NFA to DFA $($ denotes or the empty string$)3.$ Minimize the following DFA in terms of number of states $4.$ Recall that on $=\{$a$\},$ the following Finite Automaton accepts all strings of length $3$m $+5$n$,$ where m $0$ and n $0.$ Question: Design a Finite Automaton on $=\{$a$\},$ to accept all strings of length $3$m $+6$n$,$ where m $0$ and n $0,$ in three states.