Undecidability of the Emptiness Problem for Turing Machines

Here we show that the E_TM problem is undecidable. We suppose that it were decidable, then construct a decider for the A_TM problem, which cannot possibly exist. The key idea is to make a new machine that has empty language iff M accepts w.

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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