TM Design $(10$ points$)$: Our first example of a more complicated Turing machine was of $($b$)($Graded for completeness$){?}^2$ Draw a state diagram of the Turing machine you gave in part

$($a$)$ and trace the computation of this Turing machine on the input $01001000.$ You may

use all our usual conventions for state diagrams of Turing machines $($we do not include the

node for the reject state $q_{\text{r}\text{e}\text{j}}$ and any missing transitions in the state diagram have value

$(q_{\text{r}\text{e}\text{j}},,R)$;$bR$ label means $\{$:$bb,R).$

a Turing machine that recognized the language $\{w$#$w|win\{0,1{\}}^{**}\},$ which we know is not

context$-$free. The language

$\{0^k{10}^n{10}^m|0knm\}$

is also not context$-$free.

$($a$)($Graded for correctness$)1$ Give an implementation$-$level description of a Turing machine

that recognizes this language.