Can Turing Machines solve non-decision problems? Since TMs are equivalent to algorithms, they must be able to perform algoriths like, say, mergesort. But the formal definition allows only for decision problems, i.e, acceptance of languages. So how can we cast the performance of mergesort as a decision problem?
Usually, Turing machines are explained to calculate functions $f:A \rightarrow B$, of which decision problems are a special case where $B = \mathbb{B}$.