28. Design TM subroutine (i.e., a fragment of a Turing Machine), shown as a state diagram, that returns the tape head from its current position to the beginning of the tape, regardless of the contents of the tape or where the tape head was originally located. When finished, the contents of the tape must be identical to the contents when the subroutine is called. A subroutine can be shown as a machine that leaves the start symbol, performs some processing, and ends up at a single End symbol (which, when used in a larger implementation, would have an epsilon transition to the state that follows the call to the subroutine). As a subroutine, it is not required to have a halting state (though it is not prevented from having them, either). Assume that the tape alphabet includes marked and unmarked versions of every symbol and that no marked symbols are on the tape at the time this subroutine is called. Let x represent an unmarked symbol and x' represent the corresponding marked symbol. Hence a transition rule such as "x, x' > R" means that if any unmarked symbol is under the tape head, replace it with its marked counterpart and move the tape head to the right. Similarly, "X", x-> R" means that if the symbol under the tape head is marked, replace it with its unmarked version and then move the tape head to the right. Keep in mind that there is no special marker symbol at the left end of the tape - this subroutine has to function without relying on any such marker. 28. Design TM subroutine (i.e., a fragment of a Turing Machine), shown as a state diagram, that returns the tape head from its current position to the beginning of the tape, regardless of the contents of the tape or where the tape head was originally located. When finished, the contents of the tape must be identical to the contents when the subroutine is called. A subroutine can be shown as a machine that leaves the start symbol, performs some processing, and ends up at a single End symbol (which, when used in a larger implementation, would have an epsilon transition to the state that follows the call to the subroutine). As a subroutine, it is not required to have a halting state (though it is not prevented from having them, either). Assume that the tape alphabet includes marked and unmarked versions of every symbol and that no marked symbols are on the tape at the time this subroutine is called. Let x represent an unmarked symbol and x' represent the corresponding marked symbol. Hence a transition rule such as "x, x' > R" means that if any unmarked symbol is under the tape head, replace it with its marked counterpart and move the tape head to the right. Similarly, "X", x-> R" means that if the symbol under the tape head is marked, replace it with its unmarked version and then move the tape head to the right. Keep in mind that there is no special marker symbol at the left end of the tape - this subroutine has to function without relying on any such marker