Consider the Turing machine, $M,$ shown below.

$($Grafstate code for this machine is: $)$

:$+$tm TM$1$

Q$=\{$q$0,$q$1,$q$2,$q$3,$q$4,$q$5,$q$6,$q$7,$qa$,$qr$\}$

S$=\{$a$,$b$,$c$\}$

T$=\{$a$,$b$,$c$,\backslash \_,$X$,$$$\}$

q$0=$q$0$

q$0->$q$1$: a$->$$$,$R

q$0->$qr: b$->$b$,$R

q$0->$qr: c$->$c$,$R

q$0->$qr: $\backslash \_->\backslash \_,$R

q$1->$q$1$: X$->$X$,$R

q$1->$q$2$: b$->$b$,$R

q$1->$q$2$: c$->$c$,$R

q$1->$q$3$: a$->$X$,$L

q$1->$qa: $\backslash \_->\backslash \_,$L

q$2->$q$2$: b$->$b$,$R

q$2->$q$2$: c$->$c$,$R

q$2->$q$2$: X$->$X$,$R

q$2->$q$3$: a$->$X$,$L

q$2->$qr: $\backslash \_->\backslash \_,$L

q$3->$q$3$: b$->$b$,$L

q$3->$q$3$: c$->$c$,$L

q$3->$q$3$: X$->$X$,$L

q$3->$q$4$: $$->$$$,$R

q$4->$q$4$: a$->$a$,$R

q$4->$q$4$: c$->$c$,$R

q$4->$q$4$: X$->$X$,$R

q$4->$q$5$: b$->$X$,$L

q$4->$qr: $\backslash \_->\backslash \_,$L

q$5->$q$5$: a$->$a$,$L

q$5->$q$5$: c$->$c$,$L

q$5->$q$5$: X$->$X$,$L

q$5->$q$6$: $$->$$$,$R

q$6->$q$6$: a$->$a$,$R

q$6->$q$6$: b$->$b$,$R

q$6->$q$6$: X$->$X$,$R

q$6->$q$7$: c$->$X$,$L

q$6->$qr: $\backslash \_->\backslash \_,$L

q$7->$q$7$: a$->$a$,$L

q$7->$q$7$: b$->$b$,$L

q$7->$q$7$: X$->$X$,$L

q$7->$q$1$: $$->$$$,$R

$($a$)7$ points Show the computation of the string abac in this machine.

Note, abac inL$(M).$

$q_0$abac$|--$$$q_1$bac

$|--$

$($b$)8$ points Show the computation of the string accba in M$.$ Note,

accba $/$not in L$($M$).$

q$0$ accba $|--$ $q$1$ ccba

$|--$

$($c$)8$ points What is L$($M$)?$