$(35$ Points$)$ Given the following language,

$=\{|mn\}$ and $=\{0,1].$

$($a$)(10$ Points$)$ Write down the Turing Machine $($TM$)$ pseudo code

algorithm in English that recognizes $.$

$($b$)(15$ Points$)$ Build a Turing Machine, TM that recognizes $.$

$($c$)(10$ Points$)$ Specify the configuration at each single moves of TM in

$($b$)$ by step that the string $1010$ is not in $.$