$3.$ Determine whether the given machine recognizes the given input string. $(16$ points$)$

$($a$)(8$ points$)$

Input:$01110111$

n$1110111$

$($Please draw the time table how to get the output$)$

$($b$)(8$ points$)$

Input:$01101$

$($Please draw the time table how to get the output$)$