TMBR: October 2025: Difference between revisions
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* ? Oct 2025. Katelyn Doucette. [https://katelyndoucette.com/articles/building-the-busy-beaver-ladder Building the Busy Beaver Ladder]. | * ? Oct 2025. Katelyn Doucette. [https://katelyndoucette.com/articles/building-the-busy-beaver-ladder Building the Busy Beaver Ladder]. | ||
== Holdouts == | |||
* BB(7): | |||
** Andrew Ducharme has continued reducing the [[BB(7)#Phase 2|number of holdouts]] with Stage 4 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 22,721,168 holdouts remain. (0.35% reduction) | |||
*BB(3,4): | |||
**[[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]] are running filters in the domain under Phase 2, reducing the holdouts count from 434,787,751 to 64,777,377 (85.1% reduction). | |||
== Theory == | |||
TODO: Update this section after studying existing literature a bit more. | |||
[[Linear-Inequality Affine Transformation Automata]] (LIATA) were introduced as a generalization of the [[BMO1]] rules: | |||
* @Bard proved that 3 dimension LIATA are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1420457986564030641] | |||
* @star proved that 2 dimension LIATA are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1421271424588451915] | |||
* BMO1 is a 2d-LIATA so this provides some sense for the difficulty of the problem. | |||
[[Category:This Month in Beaver Research|2025-10]] | [[Category:This Month in Beaver Research|2025-10]] | ||
Latest revision as of 07:50, 4 October 2025
| Prev: September 2025 | This Month in Beaver Research | Next: November 2025 |
This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).
Blog Posts
- ? Oct 2025. Katelyn Doucette. Building the Busy Beaver Ladder.
Holdouts
- BB(7):
- Andrew Ducharme has continued reducing the number of holdouts with Stage 4 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 22,721,168 holdouts remain. (0.35% reduction)
- BB(3,4):
- XnoobSpeakable and Lúkos are running filters in the domain under Phase 2, reducing the holdouts count from 434,787,751 to 64,777,377 (85.1% reduction).
Theory
TODO: Update this section after studying existing literature a bit more.
Linear-Inequality Affine Transformation Automata (LIATA) were introduced as a generalization of the BMO1 rules: