# time complexity – Transforming multi-tape Turing machines to equivalent single-tape Turing machines

I am familiar with the fact that multi tape Turing machines have the same computational power as single tape ones. Which means every $$k$$-tape Turing machine has an equivalent single-tape Turing machine.

The question is about the computability of such a transformation and its time and space complexity:

Is there a computable function that receives as input an arbitrary multi-tape Turing machine and returns an equivalent single-tape Turing machine in polynomial time and polynomial space?