Multi-tape Turning Machine

A multi-tape turning machine is an ordinary machine that has multiple tapes. Each tape has its own tape head to read and write a single memory cell at a time. At the initial stage, the tape appears at tape 1, and others start with blank. In the next step, the machine reads its consecutive symbols and prints the symbol on each tape and moves its heads. Each head can move independently of others heads.

This machine is much more powerful than a single tape turning machine, but it needs more computation time.

Formal Definition of Multi-tape Turning machine

A multi-tape turning machine has 6-tuple -

(Q,Γ,s,b,F,δ)

Q - It is a finite set of states,
Γ - finite set of the tape alphabet,
s - initial state, (s ∈ Q),
b - blank symbol, (b ∈ Γ),
F - set of final states, (F ⊆ Q)
δ - transition function,
δ:Q x Γ^k -> Q x (Γ x {L,R,S})^k

In the above transition function, a multi tape turning machine has k-tape. So the machine stores k strings simultaneously and maintains a position in each tape of the strings.

The L, R and S are left-shift, right-shift and no-shift respectively.