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Combined display of all available logs of BusyBeaverWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 20:35, 19 August 2025 Sligocki talk contribs created page Universal Turing Machine (Created page with "A '''Universal Turing Machine''' (UTM) is a Turing Machine which can simulate any other TM (encoded onto input tape). The precise definition requires defining the encoding function to map simulated TMs and TM inputs into UTM initial tapes. Since a UTM can simulate any TM, the halting problem for any UTM is not computable. There is a common misconception that the Busy Beaver Functions will become uncomputable once we reach a domain with a UTM (since the general h...") Tag: Visual edit
- 06:00, 11 August 2025 Sligocki talk contribs created page User talk:Xl643 (Created page with "== Naming TMs == Hi Xl643, please stop adding your own personal names for TMs to their pages. The person who discovers a TM has the right to name it. Or alternatively it might be named if there is a common name used in the community. If you'd like to suggest a name in the talk page or on the Discord you are welcome but don't just add it to the page. ~~~~")
- 03:24, 9 August 2025 Sligocki talk contribs created page FAR (Redirected page to Finite Automata Reduction (FAR)) Tags: New redirect Visual edit
- 03:24, 9 August 2025 Sligocki talk contribs created page CTL (Redirected page to Closed Tape Language (CTL)) Tags: New redirect Visual edit
- 03:24, 9 August 2025 Sligocki talk contribs created page CPS (Redirected page to Closed Position Set (CPS)) Tags: New redirect Visual edit
- 18:08, 8 August 2025 Sligocki talk contribs created page 1RB0RD 0LC1RA 0RA1LB 1RE1LB 1LF1LB ---1LE (Created page with "{{machine|1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE}} {{TM|1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE}} is a non-halting BB(6) TM discovered by mxdys on 14 Sep 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1284419946759323700 Discord]) and proven non-halting the next day ([https://discord.com/channels/960643023006490684/1239205785913790465/1284838151348551795 Discord]). It follows rules similar to {{TM|1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0...")
- 22:54, 30 July 2025 Sligocki talk contribs created page File:BB6 num holdouts over time.png (Number of BB(6) holdouts over time.)
- 22:54, 30 July 2025 Sligocki talk contribs uploaded File:BB6 num holdouts over time.png (Number of BB(6) holdouts over time.)
- 15:59, 30 July 2025 Sligocki talk contribs created page 1RB0LD 1RC1RA 1LD0RB 1LE1LA 1RF0RC ---1RE (Created page with "{{machine|1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE}} {{TM|1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE}} is a probviously halting BB(6) Cryptid analzyed by mxdys on 30 July 2025. == Analysis by mxdys == [https://discord.com/channels/960643023006490684/1239205785913790465/1400141896944320602] <pre> 1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE (a,b,c) := 0^inf 1^a 0 01^b 0 11^c+1 B> 0^inf (a,2+b,c) --> (a,b,3+c) (a+1,0,c) --> (a,c,2) (a+1,1,c) --> (a,c,6) (0,0,c...")
- 01:37, 30 July 2025 Sligocki talk contribs created page BBS (Redirected page to Non-halting Turing machine#Translated cycler preperiod) Tags: New redirect Visual edit
- 01:34, 30 July 2025 Sligocki talk contribs created page BBP (Redirected page to Non-halting Turing machine#Translated cycler period) Tags: New redirect Visual edit
- 15:26, 27 July 2025 Sligocki talk contribs moved page TMiBB: July 2025 to TMBR: July 2025 (Acronym rename)
- 15:25, 27 July 2025 Sligocki talk contribs moved page Category:This Month in Busy Beaver to Category:This Month in Beaver Research (Rename to support the TMBR (Timber) acronym)
- 15:08, 27 July 2025 Sligocki talk contribs created page File:Lovecraft beaver.png (Created by Discord user Fern's friend Lauren in 2025. https://discord.com/channels/960643023006490684/992572017683472514/1398470914990936135)
- 15:08, 27 July 2025 Sligocki talk contribs uploaded File:Lovecraft beaver.png (Created by Discord user Fern's friend Lauren in 2025. https://discord.com/channels/960643023006490684/992572017683472514/1398470914990936135)
- 03:27, 27 July 2025 Sligocki talk contribs created page 1RB2LA1RA1RA 1LB1LA3RB--- (Redirected page to 1RB2LA1RA1RA 1LB1LA3RB1RZ) Tags: New redirect Visual edit
- 03:17, 27 July 2025 Sligocki talk contribs created page 1RB1LA------ 1RC3LB1RB--- 2LA2LC---0LC (Created page with "{{machine|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC}} {{TM|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC}} is the current BBi(8) champion. It runs for over <math>10^{1565}</math> steps and has a sigma score of exactly <math>\frac{3^{1642} - 11}{2}</math>. It was discovered by Nick Drozd on 26 July 2025 ([https://discord.com/channels/960643023006490684/1084047886494470185/1398753236835635252 Discord link]). == Analysis by Shawn Ligocki == <pre> A(a, b, c) = <A 2^a 0 3^b 1^...")
- 15:52, 24 July 2025 Sligocki talk contribs moved page Limited Instruction Busy Beaver to Instruction-Limited Busy Beaver (MrBrain suggested this preference since it puts the key word "Instruction" first)
- 18:36, 22 July 2025 Sligocki talk contribs created page Bouncers (Redirected page to Bouncer) Tags: New redirect Visual edit
- 18:34, 22 July 2025 Sligocki talk contribs created page MITMWFAR (Redirected page to Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR)) Tags: New redirect Visual edit: Switched
- 18:34, 22 July 2025 Sligocki talk contribs created page Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR) (Created page with "'''Meet-in-the-Middle Weighted Finite Automata Reduction''' ('''MITMWFAR''') is a Turing machine decider. It is a variation of Finite Automata Reduction (FAR) based upon Weighted Finite Automata. This allows it to decide irregular TMs which cannot be decided by FAR or any other regular decider. See: https://github.com/Iijil1/MITMWFAR/tree/main Category:Deciders Category:Stub") Tag: Visual edit
- 21:47, 16 July 2025 Sligocki talk contribs created page Limited Instruction Busy Beaver (Created page with "An '''n-instruction Turing machine''' is a Turing machine with an arbitrary number of states and symbols, but limited to only ''n'' defined transitions/instructions in its transition table (all others are undefined). The '''Limited Instruction Busy Beaver''' (BBi(n)) problem is the Busy Beaver problem limited to n-instruction TMs. So BBi(n) is the longest runtime for all halting n-instruction TMs when started on a blank tape. A TM is considered to halt as soon as it...")
- 21:00, 16 July 2025 Sligocki talk contribs created page Terminating Turmite (Created page with "A '''Terminating Turmite''' or '''Relative Movement Turing Machine''' is a Turing machine which uses relative directions instead of absolute ones. So instead of moving (L)eft or (R)ight, it (P)roceeds forward (for one step in the same direction as last move or (T)urns-around (move one direction in the opposite direction). TT(n,k) is the maximum steps of all halting n-state, k-symbol Terminating Turmites when started on a blank tape. It was coined by @creeperman7002 w...")
- 20:41, 16 July 2025 Sligocki talk contribs created page 1RB2LA2LC--- 1LA2RB2RD--- 3RB1LC1RD0LA 3LA1RD1LC0RB (Created page with "{{machine|1RB2LA2LC---_1LA2RB2RD---_3RB1LC1RD0LA_3LA1RD1LC0RB}} {{TM|1RB2LA2LC---_1LA2RB2RD---_3RB1LC1RD0LA_3LA1RD1LC0RB}} is a non-halting TT(2,4) TM that is "pretending to be" a probviously halting Cryptid. Rules by Shawn Ligocki: <pre> C(a, b, c) = 0^inf 3 2^a <C 1^b 2^c 3 0^inf = 0^inf 3 2^c 1^b D> 2^a 3 0^inf C(a+1, b, c) -> C(c, b+1, a) C(0, b, c+3) -> C(c, 0, b+6) C(0, b, 2) -> Halt(b+7) C(0, b, 1) -> C(b+5, 0, 2) C(0, b, 0) -> C(b+2, 0, 5) Start: C(1, 0, 2) @...")
- 21:32, 15 July 2025 Sligocki talk contribs created page TMiBB: July 2025 (Created page with "Category:This Month in Busy Beaver This Month in Busy Beaver for July 2025. == Champions == * (Late June) mxdys found a pair of new BB(6) champions pushing it into the pentational values: {{TM| 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE}} (scoring over 2↑↑2↑↑2↑↑10) and {{TM|1RB1LC_1LA1RE_0RD0LA_1RZ1LB_1LD0RF_0RD1RB}} (scoring over 10↑↑11010000). * mxdys confirms dyuan's BB(2,5) champion {{TM|1RB3LA4RB0R...")
- 20:56, 15 July 2025 Sligocki talk contribs created page Category:This Month in Busy Beaver (Created page with "'''This Month in Busy Beaver''' ('''TMiBB''') is a monthly series of articles dedicated to covering Busy Beaver research progress, announcements and news from each month. It is crowd-sourced, so please contribute. Shawn Ligocki is the current editor-in-chief. The article is expected to be a collection of small blurbs with links to go into more information. Process: * The articles for each month will be created around the start of the month. * Anyone ca...")
- 06:53, 13 July 2025 Sligocki talk contribs created page Bbchallenge (Redirected page to Busy Beaver Challenge) Tags: New redirect Visual edit
- 06:45, 13 July 2025 Sligocki talk contribs moved page Bbchallenge.org to Busy Beaver Challenge
- 02:59, 13 July 2025 Sligocki talk contribs created page Reversible Turing Machine (Created page with "A '''Reversible Turing Machine''' is a Turing machine for which the computation can always be run backwards from any step back to the original configuration. This property (called logical reversibility) has theoretical implications for the limits of computation. Specifically, non-reversible computation cannot scale beyond some limit due to the inherent entropy cost whereas reversible computations may be able to. == Definition == There does not seem to be a completel...") Tag: Visual edit: Switched
- 02:46, 13 July 2025 Sligocki talk contribs created page Turing Machine (Redirected page to Turing machine) Tag: New redirect
- 16:43, 9 July 2025 Sligocki talk contribs created page Num (Redirect) Tags: New redirect Visual edit
- 16:43, 9 July 2025 Sligocki talk contribs created page Maximum Consecutive Ones Function (Created page with "The '''Maximum Consecutive Ones''' function (named <math>num(n)</math> by Ben-Amram) is a Busy Beaver function which measures the maximum number of consecutive 1s left on the tape at halt across all n-state 2-symbol Turing machines which leave all their 1s consecutively. Unlike <math>\Sigma(n)</math>, this allows some amount of order over the "API" of these TMs, so that their output can be used as inputs to another TM in some deterministic fashion. Note however,...") Tag: Visual edit: Switched
- 21:05, 30 June 2025 Sligocki talk contribs created page Busy Beaver Frontier (Created page with "'''The Busy Beaver Frontier'''<ref>Scott Aaronson. 2020. [https://www.scottaaronson.com/papers/bb.pdf The Busy Beaver Frontier]. SIGACT News 51, 3 (August 2020), 32–54. https://doi.org/10.1145/3427361.3427369</ref> was a Busy Beaver survey article published by Scott Aaronson in 2020. It describes the Busy Beaver problem, introduced a number of variants (such as the Lazy Beaver and Beeping Busy Beaver) and made a number of conjectures. This article introduced ma...")
- 05:23, 7 June 2025 Sligocki talk contribs created page 1RB1RZ 0RC0RE 1LD1LA 1LC0LG 0RF1LF 0RD1LF 1LB0LE (Created page with "{{machine|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} {{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting BB(7) TM with sigma score over $10 \uparrow\uparrow 519$. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]). == Analysis by Shawn Ligocki == This TM goes through 2 phases: Phase A and Phase B. <pre> A(a, b) = 0^inf <F 10 1^a 0...")
- 14:15, 30 May 2025 Sligocki talk contribs created page Talk:Collatz-like (Definition: new section)
- 04:41, 22 May 2025 Sligocki talk contribs created page 1RB--- 0LC1RE 0LD1LC 1LE0RG 1RF0RC 1RC1RA 1RD0RB (Created page with "{{machine|1RB---_0LC1RE_0LD1LC_1LE0RG_1RF0RC_1RC1RA_1RD0RB}} {{TM|1RB---_0LC1RE_0LD1LC_1LE0RG_1RF0RC_1RC1RA_1RD0RB}} is an nonhalting BB(7) TM with an infinite tetrational rule. == Analysis by Shawn Ligocki == <pre> 11 01^n D> 00 --> 01^n+2 D> 0^4 01^2n D> 0^3 --> 111 01 0001^n 01 D> 0 01^2n+1 D> 0^4 --> 1 11^2n+2 01 D> 1000101 D> 0^5 --> 0100^2 11 01 D> 00010 01^2n D> 0^4 --> 111 01 0001^n-1 0 1^5 01 D> 0001 0101^n D> $ --> 0101^2n+6 D> $ 0001^2 0 01...")
- 03:27, 22 May 2025 Sligocki talk contribs created page 1RB1RF 0RC0RD 1LC1LD 1LE0RB 0RA1LG 1LC1RA ---0RF (Created page with "{{machine|1RB1RF_0RC0RD_1LC1LD_1LE0RB_0RA1LG_1LC1RA_---0RF}} {{TM|1RB1RF_0RC0RD_1LC1LD_1LE0RB_0RA1LG_1LC1RA_---0RF}} is an nonhalting BB(7) TM with an infinite tetrational rule. == Analysis by Shawn Ligocki == Low level rules: <pre> 11 00^n C> 0^2 --> 00^n+2 C> 1101 00^n C> 0^3 --> 0 11^n+1 00^2 C> 0010 00^n C> 0^8 --> 01 11^n+1 0^3 1 00^2 C> 001 00^n C> 0^3 --> 01 11^n 00^2 C> 110 00^n C> 0^5 --> 0^2n+3 1 00^2 C> 0101 00^n C> 0 --> 1 Z> 1^2n+4 </p...")
- 19:34, 16 May 2025 Sligocki talk contribs created page Sigma score (Redirected page to Busy Beaver Functions) Tags: New redirect Visual edit
- 19:32, 16 May 2025 Sligocki talk contribs created page BB(7) (Created page with "The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information. The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math> == History == Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed...") Tag: Visual edit
- 02:56, 14 May 2025 Sligocki talk contribs created page Fast-growing hierarchy (Redirected page to Fast-Growing Hierarchy) Tag: New redirect
- 20:09, 13 May 2025 Sligocki talk contribs created page 1RB0RA 1LC1LF 1RD0LB 1RA1LE 1RZ0LC 1RG1LD 0RG0RF (Created page with "{{machine|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} is a halting BB(7) TM which runs for over <math>2 \uparrow^{12} 2 \uparrow^{12} 3</math> steps. == Analysis by Shawn Ligocki == Consider general configurations matching the regex: <math>0^\infty \; 11 \; (1 \; (01)^*)^* \; 0011100 \; \text{A>} \; 0^\infty</math> === Low level rules === <pre> 01 1 01^n 0011100 A> 00 -->...")
- 02:40, 9 May 2025 Sligocki talk contribs created page 1RB1RA 1RC0LC 0LD1LG 1LF0LE 1RZ1LF 0LA1LD 1RA1LC (Created page with "{{machine|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}} {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}} is a halting tetrational BB(7) TM that runs for over 10↑↑35 steps found by Shawn Ligocki on 8 May 2025 based on @mxdys's enumeration system https://github.com/ccz181078/TM Analysis by Shawn Ligocki: <pre> 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC B(a,b,c,d) = 0^inf 1^a B> 1^b 01^c 011^d 0^inf D(a) = B(a,0,0,0) = 0^inf 1^a B> 0^inf D(3k) -...")
- 22:50, 28 April 2025 Sligocki talk contribs created page 1RB1RA 0RC1RC 1LD0LF 0LE1LE 1RA1LD ---0LC (Redirected page to 1RB1RA 0RC1RC 1LD0LF 0LE1LE 1RA0LB ---0LC) Tags: New redirect Visual edit
- 15:41, 28 March 2025 Sligocki talk contribs created page Busy Beaver (Redirected page to Busy Beaver Functions) Tag: New redirect
- 15:40, 28 March 2025 Sligocki talk contribs created page Busy Beaver for lambda calculus (Created page with "'''Busy Beaver for lambda calculus''' ('''BBλ''') is a variation of the Busy Beaver problem for [https://en.wikipedia.org/wiki/Lambda_calculus lambda calculus] invented by John Tromp. BBλ(n) = the maximum normal form size of any closed lambda term of size n. If you are not familiar with lambda calculus and beta-reduction, I recommend starting with that article. Size is measured in bits using [https://tromp.github.io/cl/Binary_lambda_calculus.html Binary Lambda Cal...")
- 13:29, 28 March 2025 Sligocki talk contribs created page BBλ (Redirected page to Busy Beaver for lambda calculus) Tag: New redirect
- 21:41, 25 March 2025 Sligocki talk contribs created page 1RB3LA1LA1RA3RA 2LB2RA---4RB1LB (Created page with "{{machine|1RB3LA1LA1RA3RA_2LB2RA---4RB1LB}} {{TM|1RB3LA1LA1RA3RA_2LB2RA---4RB1LB}} is a BB(2,5) TM analyzed by Racheline [https://discord.com/channels/960643023006490684/1349040227548663858/1349448649817456670 on 12 Mar 2025] that appears to be a Cryptid Analysis by Racheline: <pre> 1RB3LA1LA1RA3RA_2LB2RA---4RB1LB A(a,b) := 0^inf 1 4^a 1^3 A> 1^b 2 0^inf B(a,b) := 0^inf 1 4^a 1^b A> 1 0^inf A(a,2a+b+3) -> A(3a+4,b) A(a,2a+2) -> B(3a+4,2) A(a,2a+1) -> halt A(a,2...")
- 21:38, 25 March 2025 Sligocki talk contribs created page 1RB3LA1LA1RA1RA 2LB2RA---4RB1LB (Created page with "{{machine|1RB3LA1LA1RA1RA_2LB2RA---4RB1LB}} {{TM|1RB3LA1LA1RA1RA_2LB2RA---4RB1LB}} is a BB(2,5) TM that appears to be a Cryptid Analysis by mxdys and Racheline: <pre> 1RB3LA1LA1RA1RA_2LB2RA---4RB1LB start: A(4,4) A(a,3+a+b) --> A(4+2a,b) A(a,2+a) --> B(2a+2,3) A(a,1+a) --> halt A(b+a,b) --> B(a,2b) B(3a+1,b) --> A(4,2+5a+b) B(3a+2,b) --> B(5+5a+b,2) B(3a+0,b) --> B(3+5a+b,0) A(a,b) := 0^inf 1 4^a 1^4 A> 1^b 2 0^inf B(a,b) := 0^inf 1 4^a 1^3+b A> 11 0^inf </pre>")
- 18:06, 2 March 2025 Sligocki talk contribs created page 1RB0LE 1LC1RA ---1LD 0RB1LF 1RD1LA 0LA0RD (Created page with "{{machine|1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD}} {{TM|1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD}} is an non-halting BB(6) Turing machine. Analysis by @racheline on 29 July 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1267551868997992652 Discord link]): <pre> 1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD A(n) = 0^inf <A 0 1^n rules: A(6n) -> A(12n+3) A(6n+1) -> A(12n+6) A(6n+2) -> halt A(6n+3) -> A(9n+9) A(6n+4) -> halt A(6n+5) -> A(9...")
- 17:43, 2 March 2025 Sligocki talk contribs created page 1RB0RC 0LC0LB 0LD1LC 0LE1LA 0LF--- 1RF1RA (Created page with "{{machine|1RB0RC_0LC0LB_0LD1LC_0LE1LA_0LF---_1RF1RA}} {{TM|1RB0RC_0LC0LB_0LD1LC_0LE1LA_0LF---_1RF1RA}} is a tetrational BB(6) Cryptid found by Racheline on 30 July 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1267805112651350107 Discord link]). It is neither probviously halting or probviously non-halting. Racheline estimates that it has a 2/3 chance of become a Translated Cycler and 1/3 chance of halting eventually. <pre> 1R...") Tag: Visual edit: Switched
