$1.$ For the grammar shown below, decompose the string aaabb to all possible substrings and find the variables that generate each substring.

S $->$ AB$,$ A $->$ AB $|$ a$,$B $->$ AA $|$ b $2.(30$ points$)$ For the PDA shown below, use instantaneous description to present the complete computation that the PDA accepts the string baab. The initial instantaneous description is given by $(\backslash ($ q$\_\{0\}\backslash ),$ baab, $\backslash$$$).($Note: there are different computations for a PDA, you need to write down a computation that accepts the string.$)$

$3.(40$ points$)$ For the Turning Machine shown below, use instantaneous description to present the complete computation that the Turning Machine accepts the string aaabbb. The initial instantaneous description is given by $\backslash ($ q$\_\{0\}$ a a a b b b $\backslash ).$