Abstract
We define single- and multitape Turing machines (TMs)
and verify a translation from multitape TMs to singletape TMs. In particular, the following results have been
formalized: the accepted languages coincide, and whenever the multitape TM runs in
$\mathcal{O}(f(n))$ time, then the singletape TM has a worst-time complexity of
$\mathcal{O}(f(n)^2 + n)$.
The translation is applicable both on deterministic and non-deterministic TMs.