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(Qi, [a1, a2, a3,....]) = (Qj, [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).