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. Easy Theory Website: https://www.easytheory.org GoFundMe: https://www.gofundme.com/f/easy-theory-video-studio Patreon: https://www.patreon.com/EasyTheoryYT Fourthwall: https://easy-theory-llc-shop.fourthwall.com Problem Solving channel: ​⁠ @easytheoryprobsolve If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1