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).