# Multitape Turing machine with multiple non-blank tapes

A multitape Turing machine is defined to have input only appear on one tape, with the rest of the tapes blank.

Are there any formulations of a Turing machine that allow other tapes to be not blank? Why does the condition that the input only appears on one tape exist?

• Because it doesn't matter. You could always start with an input tape and blank working tapes and then write whatever you wanted on the working tapes before starting the actual computations. – Rick Decker Nov 21 '14 at 21:44
• Well, randomised TMs have an extra tape filled with random bits. (@RickDecker) – Raphael Nov 21 '14 at 22:06

The reason we can make this restriction is that it makes no difference to the class of functions that are computable and it also makes no significant difference to the running time of algorithms. Any interesting Turing machine algorithm is going to need linear time since, otherwise, it can't even read all its input. For example, how would a Turing machine know to halt after $\log n$ steps? It's not read all its input in that time, so it doesn't even know what $n$ is!