a$($b$|$c$)*$ a$|$aac$*$b $,$ please convert these RE to NFA then to DFA $.$ make sure to give me every step in detail like e$-$closure and moves $(($ all of them then test it $)$ Show the conversion between

a$)$ Regular Expression $$ Nondeterministic finite state automata NFA $$ deterministic finite state

automata $($DFA$)$ and from

b$)$ Regular expression $$ deterministic finite state automata $($DFA$)$ by solving an example.

c$)$ Generate and test and input strings for your example using both $($a$)$ and $($c$).$