Key takeaways:
A multi-tape Turing machine is a variant of the basic Turing machine with multiple tapes and corresponding head pointers.
Each tape can move independently, and the input is initially placed on the first tape.
It is represented as a six-tuple machine, which includes states, input alphabets, tape alphabets, transition functions, and final states.
Multiple tapes grow infinitely to the right and allow the input to be copied across the tapes for easier processing.
For example, a two-tape Turing machine can check if a string is a palindrome by copying the input onto a second tape and comparing the two tapes.
The transition functions define how the heads move and how data is updated during the process.
Multi-tape Turing machines help solve more complex problems with less computational work than a simple Turing machine.
A multiple-tape Turing machine is a variant of the simple Turing machine. It consists of multiple tapes, each having its head pointer. It can be taken as a 2D array. The heads of the multiple tapes can move in different directions independently. Initially, the input is placed in the first tape and is transferred to the other tapes as needed.
To learn more about the simple Turing machine, look into our Answer: What is a Turing machine?
Formal theorem
The multi-tape Turing machine is a six tuple machine (Q,Σ,q0,Γ,δ,F)
Q: set of states
Σ: set of input alphabets
q0: initial state
Γ: set of tape alphabets
δ: transition function that is Q ∗Γi→Q ∗Γi ∗<br>(Left,right,stationary)i
F: set of final states
Formation of the tapes
Initial multi-tapes are as follows: