$(20$ points$)$ Design a Turing machine that recognizes the language $\{$$anbm : m $2$n$\}.$ To simplify the

problem, you may assume that all inputs provided to the machine contain a single $ at the beginning.

$($Be sure that your machine rejects strings like $bab.$)$

Provide an algorithm, document your states, and provide a transition function in the form of a table.

$($Use the notation demonstrated by the next question.$)1.(20$ points$)$ Design a Turing machine that recognizes the language $\backslash (\backslash$left$\backslash \{\backslash$$ a$^\{$n$\}$ b$^\{$m$\}$: m $\backslash$geq $2$ n$\backslash$right$\backslash \}\backslash ).$ To simplify the problem, you may assume that all inputs provided to the machine contain a single $\backslash (\backslash$$ $\backslash )$ at the beginning. $($Be sure that your machine rejects strings like $\backslash$$bab.$)$

Provide an algorithm, document your states, and provide a transition function in the form of a table. $($Use the notation demonstrated by the next question.$)$