Construct a minimized DFA from the regular expression $($i$)($b$/$a$)*$aa iii$)(x+y)x(x+y{)}^{**}.$ Trace for a string $w=yx.($iv$)(a+b)(a+b{)}^{**}$ and trace for a string baaaab. $($v$)10+(0+11)0^{**}1.$