💡New BB(10) Champion at Level ω+1
BB(10) Just Got a Major Upgrade
TL;DR
A 10-state machine, n1, has become the new BB(10) champion, advancing the hierarchy to level ω+1. Its exact score is proven in Coq, marking a significant leap in computational complexity.
A 10-state machine, n1, has become the new BB(10) champion, advancing the hierarchy to level ω+1. This machine, written on 2026-10-08, beats the previous champion with a score that lies between f_(ω+1) values. For developers working with computational complexity and theoretical computer science, this marks a significant leap in understanding the limits of computation. The machine's exact score is proven in Coq, with a score of ones = 2W + 3·2↑^(W+1)(2↑^n) + 12·JJ + 5, where JJ = (3T − 13)/7 and (n, W) come from an explicit recursion. This advancement in computational theory could lead to new insights in algorithm design and computational limits.
Key Points
n1, a 10-state machine, is the new BB(10) champion, moving the hierarchy to level ω+1.
The machine's exact score is proven in Coq, with a score of ones = 2W + 3·2↑^(W+1)(2↑^n) + 12·JJ + 5.
The machine clears two units of the 7 at depth 35, writing 6T − 12 new zeros at the far left.
The machine's counter starts at 6T − 19 and loses 14 per period, reaching 7 only if T ≡ 2 (mod 7).
The machine's exact score is f_(ω+1)(JJ − 2) < ones < f_(ω+1)(6T), proving its computational superiority.
Why It Matters
If you're working on computational complexity or theoretical computer science, the new BB(10) champion at level ω+1 offers a significant leap in understanding computational limits. Researchers and developers can use this advancement to explore new algorithm designs and computational boundaries. The exact score proven in Coq provides a solid foundation for further research.
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