Design a Turing machine on the input alphabet $\{$d$,$ e$,$ f$\}$ that accepts strings represented using this Python regular expression that uses back references:"$^([$de$]*)$f$\backslash 1$$"For this machine, the final tape output does not matter. You will need to modify the tape in order to complete this exercise$\mathrm{.}2.$ Design a Turing machine on the input alphabet $\{$x$,$ y$,$ z$\}$ that removes all z characters from the input such there are no gaps. If the input string is xzzyxzy$,$ the output should be xyxy$.$ For this machine, it does not matter if the string is accepted or rejected. Hint: The final string does not need to reside on the same part of the tape where it started.