Busy beavers and Kolmogorov complexity — mentioned by tromp

Tue, 02 Jul 2024 16:44:00 GMT

> There are many variants of the original busy beaver problem, and some Busy Beaver Challenge contributors plan to keep working on these. One such variant is a functional busy beaver defined in terms of the lambda calculus [1]. Since it measures program size in bits rather than states, it allows many more values to be determined (37 so far versus only 6 for TMs), and the gap between the largest known value and values beyond Graham's Number is a mere 13 program bits. A closely related variant [2] can be directly expressed in terms of Kolmogorov complexity, which Mikhail Andreev argues [3] is…

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Busy beavers and Kolmogorov complexity — mentioned by tromp

Thu, 23 May 2024 17:43:23 GMT

Yes, 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 [2] https://arxiv.org/pdf/1703.05170

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Busy beavers and Kolmogorov complexity · HackerPapers discussions

Busy beavers and Kolmogorov complexity — mentioned by tromp

Busy beavers and Kolmogorov complexity — mentioned by tromp