TMBR: August 2025: Difference between revisions
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[[File:Conference poster for DNA31 by Tristan Stérin.png|thumb|396x396px|Conference poster for the [https://dna31.sciencesconf.org/ 31st International Conference on DNA Computing and Molecular Programming], [https://discord.com/channels/960643023006490684/960643023530762341/1409904231468761159 made by Tristan Stérin (cosmo)]]] | |||
[[:Category:This Month in Beaver Research|This Month in Beaver Research]] for August 2025, featuring plenty of holdouts reduction in numerous domains, alongside an upgraded TM-visualizer and a couple new BB adjacent games. | [[:Category:This Month in Beaver Research|This Month in Beaver Research]] for August 2025, featuring plenty of holdouts reduction in numerous domains, alongside an upgraded TM-visualizer and a couple new BB adjacent games. | ||
== Cryptids == | == Cryptids == | ||
A fast algorithm for [[Consistent Collatz]] simulation was re-discovered and popularized. Using it: | |||
* apgoucher simulated [[Antihydra]] to <math>2^{38}</math> iterations. This is actually a result from one year ago, but was rediscovered and added to the wiki. https://discord.com/channels/960643023006490684/1026577255754903572/1271528180246773883 | |||
* Shawn Ligocki simulated {{TM|1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC}} out to one additional Collatz reset, demonstrating that (if they halt, which they probviously should) they will have sigma scores <math>> 10^{10^{10^7}}</math>. | |||
== Holdouts == | == Holdouts == | ||
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*John Tromp introduced the <math>BB \lambda _1(n)</math> function for [[Busy Beaver for lambda calculus#Oracle Busy Beaver|Busy Beaver for lambda calculus with an oracle]] and computed it up to <math>BB \lambda _1(22)</math>. | *John Tromp introduced the <math>BB \lambda _1(n)</math> function for [[Busy Beaver for lambda calculus#Oracle Busy Beaver|Busy Beaver for lambda calculus with an oracle]] and computed it up to <math>BB \lambda _1(22)</math>. | ||
* Instruction-Limited Greedy Busy Beaver gBBi(n) and an [[Instruction-Limited Busy Beaver#Instruction-Limited Busy Beaver Variants|Instruction-Limited variant]] of the [[Blanking Busy Beaver]] (BLBi(n)) were introduced. gBBi(n) was computed up to n = 13 and BLBi(n) was computed up to n = 7. | * Instruction-Limited Greedy Busy Beaver gBBi(n) and an [[Instruction-Limited Busy Beaver#Instruction-Limited Busy Beaver Variants|Instruction-Limited variant]] of the [[Blanking Busy Beaver]] (BLBi(n)) were introduced. gBBi(n) was computed up to n = 13 and BLBi(n) was computed up to n = 7. | ||
== Misc == | == Misc == | ||
* Iijil shared an algorithm for converting an arbitrary n-state m-symbol TM into a 2-state TM with 3(n+1)m symbols. https://gist.github.com/Iijil1/0d611dbf0a9d52984f72cb14e66a4b28 | * Iijil shared an algorithm for converting an arbitrary n-state m-symbol TM into a 2-state TM with 3(n+1)m symbols. https://gist.github.com/Iijil1/0d611dbf0a9d52984f72cb14e66a4b28 | ||
* Carl K updated his TM web-visualizer to support multi-symbol machines. [https://carlkcarlk.github.io/busy_beaver_blaze/v0.2.6/index.html#palette=edit&colors=000000%2Cff0000%2Cffff00%2Cff00ff%2C00ffff&run=true https://carlkcarlk.github.io/busy_beaver_blaze/v0.2.6/index.html] He also extended his series of videos showing TM simulation accompanied by classical music out to some multi-symbol TMs: | * Carl K updated his TM web-visualizer to support multi-symbol machines. [https://carlkcarlk.github.io/busy_beaver_blaze/v0.2.6/index.html#palette=edit&colors=000000%2Cff0000%2Cffff00%2Cff00ff%2C00ffff&run=true https://carlkcarlk.github.io/busy_beaver_blaze/v0.2.6/index.html] He also extended his series of videos showing TM simulation accompanied by classical music out to some multi-symbol TMs: | ||
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*@mxdys Introduced "50 Random Holdouts", a thread on the Discord server, where 50 random TMs are selected from the BB(6) holdout list, and everybody focuses on these 50 machines. This month, 6/50 TMs were solved by @mxdys single-handedly. | *@mxdys Introduced "50 Random Holdouts", a thread on the Discord server, where 50 random TMs are selected from the BB(6) holdout list, and everybody focuses on these 50 machines. This month, 6/50 TMs were solved by @mxdys single-handedly. | ||
*The community (especially, Andrew Ducharme) [https://discord.com/channels/960643023006490684/992572017683472514/1408559249067479145 proposed a concept "BB(n,m) month",] where the community mainly focuses on a single domain, i.e. BB(3,3). The motive of this focused month is to make genuine progress in the one selected domain, with the ultimate goal to reduce all holdouts to [[Cryptids]], with all remaining TMs having been proven in Rocq. | *The community (especially, Andrew Ducharme) [https://discord.com/channels/960643023006490684/992572017683472514/1408559249067479145 proposed a concept "BB(n,m) month",] where the community mainly focuses on a single domain, i.e. BB(3,3). The motive of this focused month is to make genuine progress in the one selected domain, with the ultimate goal to reduce all holdouts to [[Cryptids]], with all remaining TMs having been proven in Rocq. | ||
==Blog Posts== | |||
* 1 Sep 2025. Katelyn Doucette. [https://katelyndoucette.com/articles/all-about-space-needle All About Space Needle]. | |||
==In the News== | ==In the News== | ||
* 22 Aug 2025. Ben Brubaker. Quanta Magazine. [https://www.quantamagazine.org/busy-beaver-hunters-reach-numbers-that-overwhelm-ordinary-math-20250822/ Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math]. | * 22 Aug 2025. Ben Brubaker. Quanta Magazine. [https://www.quantamagazine.org/busy-beaver-hunters-reach-numbers-that-overwhelm-ordinary-math-20250822/ Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math]. | ||
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* <code>[[1RB1LE_1LC0RA_0RF0LD_1LE1LA_1RC0LB_---1RC]]</code> ([https://bbchallenge.org/1RB1LE_1LC0RA_0RF0LD_1LE1LA_1RC0LB_---1RC bbch]): Unsolved BB(6) TM with pseudorandom behaviour | * <code>[[1RB1LE_1LC0RA_0RF0LD_1LE1LA_1RC0LB_---1RC]]</code> ([https://bbchallenge.org/1RB1LE_1LC0RA_0RF0LD_1LE1LA_1RC0LB_---1RC bbch]): Unsolved BB(6) TM with pseudorandom behaviour | ||
[[Category:This Month in Beaver Research]] | [[Category:This Month in Beaver Research|2025-08]] | ||
Revision as of 13:29, 2 September 2025
This Month in Beaver Research for August 2025, featuring plenty of holdouts reduction in numerous domains, alongside an upgraded TM-visualizer and a couple new BB adjacent games.
Cryptids
A fast algorithm for Consistent Collatz simulation was re-discovered and popularized. Using it:
- apgoucher simulated Antihydra to iterations. This is actually a result from one year ago, but was rediscovered and added to the wiki. https://discord.com/channels/960643023006490684/1026577255754903572/1271528180246773883
- Shawn Ligocki simulated
1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC(bbch) out to one additional Collatz reset, demonstrating that (if they halt, which they probviously should) they will have sigma scores .
Holdouts
In August there were significant reductions in Holdouts lists across many BB Domains
| Domain | New Holdout Count | July Holdout Count | # TMs Decided | % Reduction |
|---|---|---|---|---|
| BB(6) | 2,592 | 2,728 | 136 | 5.0% |
| BB(2,6) | 18,054,938 | 22,302,296 | 4,247,358 | 19.0% |
| BB(7) | 59,727,905 | 86,129,304 | 26,401,399 | 30.7% |
- BB(6) holdouts: Reduced by a total of 136 holdouts by 4 people.
- XnoobSpeakable found 9 new halting TMs in the high exponential runtime range (~) by running Enumerate.py out to extremely high parameters. https://discord.com/channels/960643023006490684/1239205785913790465/1401470301467836556
- Andrew Ducharme found a surprisingly short running halting TM in the BB(6) holdouts list with runtime ~, to which Peacemaker replied with another TM that was almost identical, and soon, simulation showed it to halt in the same number of steps. Later on the 28th, Ducharme found another one with surprisingly low runtime: ~. In response, Peacemaker found an almost identical machine, which also halts with similar runtime.
- Peacemaker shared a list of BB(6) holdouts and how many steps are required to use all defined transitions. https://discord.com/channels/960643023006490684/1239205785913790465/1410437756777398344
- @mxdys shared a list of 7 holdouts that he solved using his RWLAcc decider in Rocq (previously known as Coq). https://discord.com/channels/960643023006490684/1239205785913790465/1408304281039409212 He also shared results featuring 6 holdouts that were solved in "50 Random Holdouts", see https://discord.com/channels/960643023006490684/1400456788955893840/1409115537631613020
- On August 30, @mxdys shared the new holdouts list, consisting of 2,592 TMs. (The additional 110 TMs not listed here were solved by @mxdys using deciders.)
- After the enumeration of BB(7) was completed, Andrew Ducharme ran several deciders on the holdouts list, filtering the original 86,129,304 holdouts down to 59,727,905 in 10 days. https://drive.google.com/drive/u/0/folders/17U0BRpJHTMLtB0poBlOSZhGGp4FkCHIO
- BB(3,3): 9 holdouts were proven non-halting in Rocq (previously known as Coq) by mxdys. 10 holdouts remain, 4 of them solved with moderate rigor. https://discord.com/channels/960643023006490684/1259770474897080380/1410308974275985428
- @mxdys proved 2 BB(2,5) machines are non-halting in Rocq.
- Andrew Ducharme reduced the BB(2,6) holdouts from 22,302,296 to 18,054,938. https://discord.com/channels/960643023006490684/1084047886494470185/1412345770241163294
BB Adjacent
- John Tromp introduced the function for Busy Beaver for lambda calculus with an oracle and computed it up to .
- Instruction-Limited Greedy Busy Beaver gBBi(n) and an Instruction-Limited variant of the Blanking Busy Beaver (BLBi(n)) were introduced. gBBi(n) was computed up to n = 13 and BLBi(n) was computed up to n = 7.
Misc
- Iijil shared an algorithm for converting an arbitrary n-state m-symbol TM into a 2-state TM with 3(n+1)m symbols. https://gist.github.com/Iijil1/0d611dbf0a9d52984f72cb14e66a4b28
- Carl K updated his TM web-visualizer to support multi-symbol machines. https://carlkcarlk.github.io/busy_beaver_blaze/v0.2.6/index.html He also extended his series of videos showing TM simulation accompanied by classical music out to some multi-symbol TMs:
- Bigfoot: https://youtu.be/YvOHWbQNMoY
- Brady's Surprise in a Box: https://youtu.be/vIG2CvJShRc
- BB(2,5) champ: https://youtu.be/QpYBzYDdLEY
- Some interesting BB(2,5) machines: https://youtu.be/CSEKxTpXrDE
- @mxdys Introduced "50 Random Holdouts", a thread on the Discord server, where 50 random TMs are selected from the BB(6) holdout list, and everybody focuses on these 50 machines. This month, 6/50 TMs were solved by @mxdys single-handedly.
- The community (especially, Andrew Ducharme) proposed a concept "BB(n,m) month", where the community mainly focuses on a single domain, i.e. BB(3,3). The motive of this focused month is to make genuine progress in the one selected domain, with the ultimate goal to reduce all holdouts to Cryptids, with all remaining TMs having been proven in Rocq.
Blog Posts
- 1 Sep 2025. Katelyn Doucette. All About Space Needle.
In the News
- 22 Aug 2025. Ben Brubaker. Quanta Magazine. Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math.
Interesting TMs
A collection of interesting TMs that were mentioned on Discord, mostly because of their space-time diagrams or general behavior.
1RB0LE_1RC0RF_1RD---_0LA1RB_1RB1LE_1LD1RF(bbch): Wavy Machine1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE(bbch): Probviously halting cryptid1RB1LE_1LC0RA_0RF0LD_1LE1LA_1RC0LB_---1RC(bbch): Unsolved BB(6) TM with pseudorandom behaviour