Consider the Turing Machine $($TM$)$ T $($over the input alphabet $\backslash$Sigma $=\{$a$,$ b$\})$ given below.

$($b$,$ B$,$ R$)$

$($a$,$ a$,$ R$)($b$,$ X$,$ R$)$

$($b$,$ b$,$ R$)$

$(\backslash$Delta $,\backslash$Delta $,$ R$)$

Hint: Trace the execution of the TM on a few strings of as and bs so that you can see how it works.

$($a$)$

What is the shortest word that would be accepted by T $?(1)$

$($b$)$

What is accept$($T $)?(2)$

$($c$)$

What is reject$($T $)?(1)$

$($d$)$

What is loop$($T $)?(2)$