Why Calculating the Maximum Space Used by Turing Machines Is Impossible 🧠

Here we show that determining the maximum space used by Turing Machines of a particular type on inputs of some size is not computable, with the main technique being the recursion theorem (see the main video on that here: https://www.youtube.com/watch?v=iXpp5X6WPkE&ab_channel=EasyTheory).

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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.