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I am learning about Turing machines. I understand the alphabet set of symbols and the states a machine can be in. However, I do not understand how the transition function works.

I come from a maths background and functions always follow a simple input output. The table of transtions seems out of place.

How does a computer read a table as a function?

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    $\begingroup$ Discrete functions can be represented by a table. $\endgroup$
    – user16034
    Mar 11, 2023 at 20:36
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    $\begingroup$ I don't see a table as "out of place" in mathematics. We learn multiplying by memorizing a 10x10-table and when we are adult we switch to group tables. Truth tables. Databases. Adjacency matrices. $\endgroup$ Mar 12, 2023 at 14:13

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You can think of a function $f:S\times \Sigma \rightarrow S$ as a "table", where the rows are elements of $S$, the columns are elements of $\Sigma$, and the cell's contents is the result $f(s,\sigma)\in S$ of the $s$ of the current row, and the $\sigma$ of the current column.

This is just a more convenient way to write complex transition functions and doesn't have a real semantic meaning.

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