Talk:Champions: Difference between revisions
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(Created page with "==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 (symb...") |
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==Larger champions== | ==Larger champions== | ||
What are the known two-symbol champions beyond | What are the known two-symbol champions beyond BB(16)? Vielhaber, Chacón, and Ceballos's paper "[https://arxiv.org/abs/2303.02855v1 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 [https://googology.miraheze.org/wiki/Block_subsequence_theorem block subsequence function], but this is a very large jump up in state count from 14 states for f<sub>ω+1</sub>(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.) [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 22:00, 17 August 2024 (UTC) | ||
Revision as of 22:02, 17 August 2024
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 fω+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)