Assume the Universal Turing Machine $($U T M $)$ is given input $$M$,$ w$,$

where w $=$ abba.

$($a$)11$ points Show the contents of U T M before starting the simula$-$

tion of the first step M $,$ but after initializing all the tapes. I.e$.,$

show the tape contents of U T M upon the first visit to line $4$ of the

pseudo$-$code in the Chapter $4\mathrm{.}2$ Video $1$ slide titled $$Simulating a

TM$.$ Be sure to indicate where the tape heads are for each tape.

You can just use $$M $$ to indicate the string representing M $.$ As$-$

sume M $$s start state is q$0.$

$($b$)11$ points Assume that after several steps of M $$s computation,

the configuration would be AXq$\_$iY bb$,$ and assume that in M $,$

$\backslash$delta $($q$\_$i$,$ Y $)=($q$\_$j $,$ Z$,$ R$).$ Show the tape contents $($and tape head

locations$)$ of UTM before and after taking this transition. Once

again, this means the tape contents when UTM is on line $4.$