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At a high level, wouldn’t you expect Champions to be chaotic in the limit? As in, the halting problem tells us that any increasing sequence of Champions is not
by kevinventullo 2y ago
At a high level, wouldn’t you expect Champions to be chaotic in the limit? As in, the halting problem tells us that any increasing sequence of Champions is not computable.
- tromp 2y agoYes, for a busy beaver properly defined in information theoretic terms, like BBλ2 [1], one can prove that its champions must be incompressible up to some constant. Mikhail Andreev's article "Busy Beavers and Kolmogorov complexity" [2] explores these connections. [1] https://oeis.org/A361211 https://oeis.org/A361211 [2] https://arxiv.org/pdf/1703.05170 https://arxiv.org/pdf/1703.05170