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What is the link between the language defined by the Turing Machine and the algorithm that the Turing machine implements?

I.e. What is the link between the language and the algorithm

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A Turing Machine implements an algorithm.

The algorithm will either accept, reject or loop forever on certain inputs.

If we collect all of the inputs that the Turing Machine halts and accepts on. This is the associated language recognised by the Turing Machine.

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