Undecidability of Turing Machine Equivalence 🤖

Here we show that the EQ_TM problem is undecidable. Supposing that it were decidable, we show that the E_TM (emptiness) problem is decidable, but in reality it is not.

What is a Turing Machine? It is a state machine that has a set of states, input, tape alphabet, a start state, exactly one accept state, and exactly one reject state. See https://www.youtube.com/watch?v=j0bIxPqlYLE&ab_channel=EasyTheory for more details.

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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.