a$)$ Design a Finite state machine for a language, ${}^{+}=\{0,1\},$ that accepts strings containing substring $\text{'}010\text{'}$ in the middle and substring $\text{'}11\text{'}$ in the end of every pattern.

b$)$ Write down the regular expression for the machine in PART A using Arden's Theorem

c$)$ Convert the NFA produced in PART A into DFA.

d$)$ Convert the following NFA into DFA

$\backslash$table$[[,0,1],[->$A$,\{$B$,$C$\},\{$C$\}],[$B$,\{$A$\},\{$C$,$D$\}],[$C$,-,\{$E$\}],[**$D$,\{$A$,$D$\},\{$B$\}],[$E$,\{$A$,$B$,$E$\},\{$E$\}]]$

e$)$ Design the Regular expression for the given DFA using Arden's Theorem