Emptiness for Turing Machines is Undecidable

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    • Turing Machines - what are they? + Fo...   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.