Talk:Champions

Larger champions

What are the known two-symbol champions beyond \(BB(16)\)? Vielhaber, Chacón, and Ceballos's paper "Friedman's 'Long Finite Sequences': The End of the Busy Beaver Contest" gives a \(2450\)-state two-symbol busy beaver halting after at least \(n(4)\) steps, where \(n\) is Friedman's block subsequence function, but this is a very large jump up in state count from \(14\) states for \(f_{\omega+1}(65536)\). (This paper has some mistakes with their (symbol,state count) notation for TMs, for example referring to Aaronson's and Yedidia's machine as a (7910,2) machine rather than a (2,7910) machine, so maybe the machine whose state count I wrote here is the wrong one.) C7X (talk) 22:00, 17 August 2024 (UTC)