Turing machines:

$[25$ marks$]$

$($a$)$ Design a Turing machine to accept the following language over the alphabet

$[18$ marks$]\{0,1,2\}$:$L=\{0^n{1}^n{2}^n|n1\}.$ Ensure you include a description of your algorithm.

$($b$)$ Show how the Turing machine processes the string $001122.$

$[7$ marks$]$