$1$a$.$ Use computation histories to show decidability for the language

$A_{\text{D}\text{F}\text{A}}=\{($:$M,w$:$)|Mis$ a DFA that accepts string $w\}$

$1$b$.$ Give the computation history for $M_2$ in Figure $1$ on string $w=0000.$Figure $1$: State Transition Diagram for $M_2.$

$1$c$.$ Let $M=(Q,,,,q_0,q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}}),$ where $Q=\{q_1,q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}},q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}}\},=\{0,1\},$

$=\{0,1,\},(q_1,0)=(q_1,-,S),(q_1,1)=(q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},-,S),q_0=q1,q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}}=q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},$

and $q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}}$ is implicit, and the $\text{'}-\text{'}$ means no write is performed. Show the computation

history of $M$ on $w=011.$