Final answer:
The student is tasked with creating a multitape Turing machine to decide the language consisting of strings of the form w#w, where w belongs to the set of strings composed of 'a' and 'b'. This machine will read the input, use a separate tap for comparison, and decide if the string is in the correct form where w repeats exactly before and after the # separator.
Step-by-step explanation:
The question pertains to the design of Turing machines for a computation theory class. Turing machines are abstract computing devices that use a system of rules to operate on an infinite tape that represents the memory of a computer. Specifically, the task is to create a multitape Turing machine that decides the language L = {w#w : w ∈ Σ*} with Σ = {a,
b}. This implies the creation of a machine that accepts strings of the form w#w where w is any string composed of symbols from Σ, and # is a separator symbol. The comment annotations in a Turing machine's description are important for understanding the purpose and mechanics of each state and transition within the machine.
Creating a Multitape Turing Machine for L = {w#w}:
Initialize two tapes: one for input and another for comparison.
Read input from the first tape and copy it onto the second one until the separator # is reached.
After the separator, continue to read the remaining input on the first tape and simultaneously compare it to characters from the second tape.
If all characters match and both tapes reach the end of the string at the same time, enter an accept state; otherwise, reject the string.
The multitape Turing machine concept is a generalization of the standard Turing machine, which provides additional computational resources that can simplify some types of computations.