Multi-track Turing Machine

Multi-track Turing machines, a specific type of Multi-tape Turing machine, contain multiple tracks but just one tape head reads and writes on all tracks. Here, a single tape head reads n symbols from n tracks at one step. It accepts recursively enumerable languages like a normal single-track single-tape Turing Machine accepts.

A Multi-track Turing machine can be formally described as a 6-tuple (Q, X, ∑, δ, q₀, F) where −

• Q is a finite set of states

• X is the tape alphabet

• ∑ is the input alphabet

• δ is a relation on states and symbols where

  δ(Q_i, [a₁, a₂, a₃,....]) = (Q_j, [b₁, b₂, b₃,....], Left_shift or Right_shift)

• q₀ is the initial state

• F is the set of final states

Note − For every single-track Turing Machine S, there is an equivalent multi-track Turing Machine M such that L(S) = L(M).