Turing machine acceleration refers to using high level understanding of specific properties of specific Turing machines to be able to simulate them much fatser than naively running the simulation as usual.
Acceleration allows one to use simulation to find infinite loops that might be very long, and would not be otherwise spotted without acceleration.
This is for example the case of www.sligocki.com/2023/03/13/skelet-1-infinite.html proof of Skelet machine #1.
This notation is cool as it gives the spin quantum number, which is important e.g. when talking about hyperfine structure.
But it is a bit crap that the spin is not given simply as but rather mixes up both the azimuthal quantum number and spin. What is the reason?
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