Q$4.$ Design an NFA from the given Regular Expression $[$a $($a ba$*)*].$ Write the step$-$by$-$step construction.

Q$5.$ Consider a language $L$ over $\{a,b\},$ that accepts all strings of length three. Design a nondeterministic finite automaton which recognizes L$.$ Convert it to DFA. Write the tuple form, transition table, transition diagram.