Final answer:
The question requests the construction of a Turing Machine that duplicates an input string w and inserts a '#' symbol between the original and the copy, ending with the head at the '#'. The Turing Machine will perform a series of steps, moving across the tape and manipulating symbols to duplicate the string and insert the separator symbol. The description provides a high-level guide to designing such a TM.
Step-by-step explanation:
A student has asked for the construction of a Turing Machine (TM) that takes an input w=w₀ w₁ …wₙ and produces the output w#w. In the world of theoretical computer science, a Turing Machine is a mathematical model of computation that defines an abstract machine. This machine manipulates symbols on a strip of tape according to a table of rules. To achieve the task of duplicating the string w and inserting a '#' symbol in between, we can design a TM with multiple states to move across the tape, read and write symbols, and keep track until it completes the process with its head positioned at the '#' symbol.
Here is a high-level description of such a TM:
- Start in the initial state on the first symbol of w.
- Move right, looking for a blank symbol that indicates the end of the input w.
- When the end is found, write a '#' symbol.
- Move back to the start of w, and begin copying symbols to the right of '#' one by one.
- After copying each symbol, use different states to navigate back and forth between the copied and original parts ensuring accurate duplication without confusion.
- Once the entire string is duplicated, enter a final state with the head over the '#' symbol, marking the end of computation.
This is a simplified description and implementing it requires detailed state transitions and handling edge cases.