[arethuza]

Also worth noting that, from a practical perspective, even very simple programs/TMs can exhibit very complex behaviours that make it difficult to work out whether they will actually halt or not.

At the time of writing there are 2833 5 state binary TMs that haven't been decided yet:

https://github.com/bbchallenge/bbchallenge-undecided-index/b...

[SkiFire13]

This comment really didn't age well https://discuss.bbchallenge.org/t/july-2nd-2024-we-have-prov...

[arethuza]

Ha! - I had no idea thanks

[SkiFire13]

To be fair, the announcement I linked was published 2 hours after your comment. It was just perfect timing.

[jononor]

That is a much lower complexity grade than I thought we would struggle with. Especially since we have decades of experience in solvers for rather large Boolean Satisfiability Problems, which seems like it could be adapted here.

[kragen]

bounded model checking is indeed a thing, but it's bounded

[arethuza]

A few months back I spent a couple of hours writing a binary TM simulator (yes I know you can download them - I wanted to write one) and then spent a couple of weeks running various TMs for days on end...

They exhibit quite bizarre amounts of complexity for what are really simple structures - indeed some TMs have apparently been observed employing Collatz conjecture type behaviour.

[kragen]

awesome!

[ted_dunning]

Apparently, there is news on this:

https://www.quantamagazine.org/amateur-mathematicians-find-f...

Not sure why that github still lists so many undecideds.