A Multitrack Turing machine is a specific type of multi-tape Turing machine. In a standard n-tape Turing machine, n heads move independently along n tracks. In a n-track Turing machine, one head reads and writes on all tracks simultaneously. A tape position in an n-track Turing Machine contains n symbols from the tape alphabet. It is equivalent to the standard Turing machine and therefore accepts precisely the recursively enumerable languages.

Formal definition

A multitrack Turing machine with n-tapes can be formally defined as a 6-tuple, where A non-deterministic variant can be defined by replacing the transition function \delta by a transition relation.

Proof of equivalency to standard Turing machine

This will prove that a two-track Turing machine is equivalent to a standard Turing machine. This can be generalized to a n-track Turing machine. Let L be a recursively enumerable language. Let be standard Turing machine that accepts L. Let M' is a two-track Turing machine. To prove M=M' it must be shown that and. If the second track is ignored then M and M' are clearly equivalent. The tape alphabet of a one-track Turing machine equivalent to a two-track Turing machine consists of an ordered pair. The input symbol a of a Turing machine M' can be identified as an ordered pair [x,y] of Turing machine M. The one-track Turing machine is: This machine also accepts L.