# Multi-track Turing Machine - Proof of Equivalency To Standard Turing Machine

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 M= be standard Turing machine that accepts L. Let M' is a two-track Turing machine. To prove M=M' it must be shown that M M' and M' M

If all but the first track is ignored than 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 of Turing machine M. The one-track Turing machine is:

M= with the transition function

This machine also accepts L.

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