# AVerified Translation of Multitape Turing Machines Into Singletape Turing Machines

November 30, 2022

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### 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.