Undecidability of Determining Regular Languages in Turing Machines 🤖

Here we show the problem of checking if a Turing Machine has regular language is undecidable (or CFL as its language), called Regular_TM. The idea is similar to showing E_TM undecidable in that we suppose it is decidable, then build a decider for A_TM.

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.