Turing Machine Notation and Normal Form

1. One question about busy beavers is: is there a unique halting n-state TM of maximal runtime? The answer is obviously no, since every program can be modified by shuffling states, etc. So the question needs some caveat to exclude uninteresting variations. There doesn't seem to have been a good definition of that up to now, where "good" means "precise and reliable".

2. If you are searching for certain Turing machines, like busy beaver candidates, one strategy would be to generate all possible programs and then filter for certain properties. This definition makes for an easy filter. It might even be possible to define with a regexp.

3. Emailing. Yes, believe it or not, I personally have emailed Turing machine programs to other people in the past few months.

Of course, I'm not saying that these are particularly important problems to solve, but if you search for Turing machines, they're problems you might deal with. Check out this historical list of busy beaver candidate programs [2].

[1] https://www.scottaaronson.com/blog/?p=4916

[2] http://www.logique.jussieu.fr/~michel/ha.html