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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).
- 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
- 16:51, 2 March 2025 Sligocki talk contribs created page 1RB0RD 0RC1RE 1RD0LA 1LE1LC 1RF0LD ---0RA (Created page with "{{machine|1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA}} {{TM|1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA}} is a probviously halting tetrational BB(6) Cryptid found by Racheline on 1 Mar 2025 ([https://discord.com/channels/960643023006490684/1239205785913790465/1345551751016878272 Discord link]). <pre> f(3n) = 8n+3 f(3n+1) = 8n+11 f(3n+2) = 8n+12 a_0 = 4 a_(n+1) = f(a_n) b_0 = 0 b_(n+1) = b_n+(1 if 3|a_n else 2) c_0 = 14(?) c_(n+1) is somewhere around the smalles...")
- 16:47, 2 March 2025 Sligocki talk contribs created page 1RB0LC 1LC0RD 1LF1LA 1LB1RE 1RB1LE ---0LE (Created page with "{{machine|1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE}} {{TM|1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE}} is a probviously halting tetrational BB(6) Cryptid found by Racheline on 23 Nov 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1310044618632593409 Discord link]). <blockquote> 1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE is a tetrational probviously halting cryptid. the lower bound for when it halts is around 10^10^120395, and with...")
- 16:43, 2 March 2025 Sligocki talk contribs created page 1RB1LE 0LC0LB 1RD1LC 1RD1RA 1RF0LA ---1RE (Created page with "{{machine|1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE}} {{TM|1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA}} is a tetrational BB(6) Cryptid found by Racheline on 30 July 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1267788732300398647 Discord link]). It is the first discovered Cryptid which is neither probviously halting or probviously non-halting. Racheline estimates that it has a 3/5 chance of become a Translated Cycler and 2/5 c...")
- 16:38, 2 March 2025 Sligocki talk contribs created page 1RB0LC 0LC0RF 1RD1LC 0RA1LE ---0LD 1LF1LA (Created page with "{{machine|1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA}} {{TM|1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA}} is a probviously halting tetrational BB(6) Cryptid found by Racheline on 30 July 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1267778444280725514 Discord link]). <pre> 1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA A(n,m) = 0^inf 1^n 0 F> (01)^m 0^inf A(2n,m) -> A(3n+6,m-3) A(2n+1,m) -> A(3n+4,m-1) A(2n,2) -> A(3n+5,0) A(2n+1,0) ->...")
- 16:31, 2 March 2025 Sligocki talk contribs created page 1RB0RE 1LC1LD 0RA0LD 1LB0LA 1RF1RA ---1LB (Created page with "{{machine|1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB}} {{TM|1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB}} is a probviously halting tetrational BB(6) Cryptid found by Racheline on 30 July 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1267752546546487357 Discord link]). <pre> 1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB A(n,m) = 0^inf (01)^(3n-4) A> (01)^m 0^inf A(2n,m) -> A(3n,m-2) A(2n+1,m) -> A(3n+1,m-1) A(n,0) -> A(2,3n-4) A(n,-1) -...")
- 16:23, 2 March 2025 Sligocki talk contribs created page 1RB1RE 1LC1LD ---1LA 1LB1LE 0RF0RA 1LD1RF (Created page with "{{machine|1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF}} {{TM|1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF}} is a probviously halting tetrational BB(6) Cryptid. found by Racheline on 29 July 2024 [https://discord.com/channels/960643023006490684/1239205785913790465/1267538388530233404 Discord link]. <pre> 1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF A(m, n+9) = 0^inf 1^m (01)^n 0 A> 0^inf rules: A(m+4, 2n) -> A(m, 3n) A(m+4, 2n+1) -> A(m, 3n+1) A(0, 2n) -> halt A(0,...")
- 15:24, 27 February 2025 Sligocki talk contribs created page 1RB2LA1LA 2LA0RA2RC ---1RB2RA (Redirected page to 1RB2LA1LA 2LA0RA2RC ---0LC2RA) Tag: New redirect
- 03:35, 17 February 2025 Sligocki talk contribs created page User talk:MrSolis (Created page with "== Antihydra == Hi, I rolled back your recent change to Antihydra because it seems like you removed a ton of content there. Feel free to add your proofs if you'd like, but no need to remove the transition table and so much of the description. ~~~~")
- 18:04, 16 February 2025 Sligocki talk contribs created page Least busy beaver (Created page with "The '''least busy beaver''' <math>BB^-(n, m)</math> problem is a variation of the busy beaver problem which considers TM behavior across all starting tapes (not just blank tapes like the traditional BB problem) invented by racheline on 15 Feb 2025. == Definition == Let <math>BB_{init}(n, m, T)</math> be the longest runtime for all n-state m-symbol TMs which halt when started on tape configuration T (where T is allowed to be any infinite tape configuration, including one...")
- 00:26, 9 February 2025 Sligocki talk contribs created page 1RB1LA 1RC1LE 1RD1RE 0LA1RC ---0LB (Redirected page to 0RB1LD 1LC1RB 1LD1RE 1LA1LE 1LZ0RC) Tag: New redirect
- 00:25, 9 February 2025 Sligocki talk contribs created page 1RB1LA 1RC1LE 1RD1RE 0LA1RC 1RZ0LB (Redirected page to 0RB1LD 1LC1RB 1LD1RE 1LA1LE 1LZ0RC) Tag: New redirect
- 00:25, 9 February 2025 Sligocki talk contribs created page 0RB1LD 1LC1RB 1LD1RE 1LA1LE 1RZ0RC (Redirected page to 0RB1LD 1LC1RB 1LD1RE 1LA1LE 1LZ0RC) Tag: New redirect
- 00:25, 9 February 2025 Sligocki talk contribs created page 0RB1LD 1LC1RB 1LD1RE 1LA1LE ---0RC (Redirected page to 0RB1LD 1LC1RB 1LD1RE 1LA1LE 1LZ0RC) Tags: New redirect Visual edit: Switched
- 00:20, 9 February 2025 Sligocki talk contribs created page 0RB1LD 1LC1RB 1LD1RE 1LA1LE 1LZ0RC (Created page with "{{machine|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} {{TM|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the num(5) champion (the BB(5) TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho. It halts after 15590 steps with tape <math>0^\infty <Z 1^{165} 0^\infty</math> == Analysis by Shawn Ligocki == <pre> A(a, b) = $ 1^a <A 11^b $ A(a+3, b) -> A(a, b+2) A(0, b) -> A(2b, 1) A(1, b) -> A(0, b+1) A(2, b) -> $ <Z 1^{...")
- 19:47, 7 February 2025 Sligocki talk contribs created page 0RB1RZ0RB 1RC1LB2LB 1LB2RD1LC 1RA2RC0LD (Created page with "{{machine|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}} {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} is a halting BB(4,3) machine that appears to run for around <math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)</math> steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the ma...") Tag: Visual edit
- 19:24, 6 February 2025 Sligocki talk contribs created page Skelet (Create page for Skelet) Tag: Visual edit
- 19:04, 6 February 2025 Sligocki talk contribs created page Coq-BB5 (Created page with "Coq-BB5 is a Coq proof that BB(5) = 47,176,870. It combines many deciders and individual TM proofs that the bbchallenge.org community developed and described over the years 2022-2024. It is maintained by mxdys and includes a snapshot of BusyCoq maintained by meithecatte. See: https://github.com/ccz181078/Coq-BB5/tree/main Category:Stub") Tag: Visual edit
- 18:26, 6 February 2025 Sligocki talk contribs created page Category:BB Domain (Created page with "A Busy Beaver "Domain" is "BB(n, k)" for a specific choice of n and k. In other words, it's the Busy Beaver problem restricted to a specific number of states and symbols.") Tag: Visual edit
- 18:23, 6 February 2025 Sligocki talk contribs created page BB(4,3) (Created page with "TODO == Potential Champions == In May 2024, Pavel Kropitz found 7 halting TMs that run for a large number of steps, but have not been analyzed in detail:<pre> Halt(SuperPowers(2)),2,0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD,4,6,0,0,36,11,0,20175,2303,1 2^((80*2^((<(8*2^((8*2^(29) - 2)) - 5); (<(80*2^((b - 10)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4); (<(80*2^((<(80*2^((8*2^((8*2^(29) - 2)) - 3)) - 13)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (4...") Tag: Visual edit
- 03:34, 6 February 2025 Sligocki talk contribs created page 1RB3LA4RB0RB2LA 1LB2LA3LA1RA--- (Redirected page to 1RB3LA4RB0RB2LA 1LB2LA3LA1RA1RZ) Tag: New redirect
- 03:34, 6 February 2025 Sligocki talk contribs created page 1RB1RA 1LC1RF 1RE1LD 0RD1LB ---0RA ---0LE (Redirected page to 1RB1RA 1LC1RF 1RE1LD 0RD1LB ---0RA 1RZ0LE) Tag: New redirect
- 03:33, 6 February 2025 Sligocki talk contribs created page 1RB0RC 1LC1LF 1RD0LB ---0LE ---1RA 1LB0RE (Redirected page to 1RB0RC 1LC1LF 1RD0LB 1RZ0LE ---1RA 1LB0RE) Tag: New redirect
- 03:32, 6 February 2025 Sligocki talk contribs created page 1RB0RF 1LC1RB 0RD0LB 1RZ0LE 1RE0RA 1RD1RE (Created page with "{{machine|1RB0RF_1LC1RB_0RD0LB_1RZ0LE_1RE0RA_1RD1RE}} {{TM|1RB0RF_1LC1RB_0RD0LB_1RZ0LE_1RE0RA_1RD1RE}} halts with roughly <math>2^{2^{97/3}}</math> steps. == Analysis by racheline == https://discord.com/channels/960643023006490684/1239205785913790465/1336829029948588113 It halts with roughly 2^(2^96/3)/3 1s on the tape and after roughly 2^(2^97/3) steps. it follows these rules: <pre> A(n,m) := 111 E> 1^(3n) 0 1^m A(n,6m+1) -> A(n+2m+1,2^(n+2m)+2^((2^(2m)-1)/3)+1) A(n,...")
- 03:28, 6 February 2025 Sligocki talk contribs created page 1RB0RF 1LC1RB 0RD0LB ---0LE 1RE0RA 1RD1RE (Redirected page to 1RB0RF 1LC1RB 0RD0LB 1RZ0LE 1RE0RA 1RD1RE) Tag: New redirect
- 22:07, 5 February 2025 Sligocki talk contribs created page 1RB0LD 1RC0RC 1LA0RD 1RC1LE 0LF--- 1LA0RC (Created page with "{{machine|1RB0LD_1RC0RC_1LA0RD_1RC1LE_0LF---_1LA0RC}} {{TM|1RB0LD_1RC0RC_1LA0RD_1RC1LE_0LF---_1LA0RC}} is non halting. It is equivalent to {{TM|1RB0RC_1RC1LE_1LD0RB_1RA0LB_0LF---_1LD0RF}} == Analysis by @nerdyjoe == These two machines are non-halting. After a brief stabilization period, it works as a ternary counter with some fun behavior. The head sweeps left and right. Each bounce off the left side extends the meta-tape by one, each pass to the right "adds one" and e...")
- 20:19, 5 February 2025 Sligocki talk contribs created page 1RB1RC 1LC1RE 1LD0LB 1RE1LC 1LE0RF ---1RA (Created page with "{{machine|1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_---1RA}} {{TM|1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_---1RA}} Current second longest running BB(6) TM discovered by @racheline on 25 Nov 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1310651468881334394 Discord Link]). It runs for over <math>10 \uparrow\uparrow 7</math> steps. == Analysis by racheline == <pre> a_1 = (2^179+1)/3+179 a_2 = (2^a_1+1)/3+a_1 a_3 = (2^a_2+1)/3+a_2 a_4 = (2^a_3+1)/3+a_3...")
- 17:48, 16 January 2025 Sligocki talk contribs created page 1RB3LA4RB0RB2LA 1LB2LA3LA1RA1RZ (Created page with "{{machine|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ}} {{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ}} This is the current BB(2,5) champion. It halts with sigma score (and runtime) over <math>10^{10^{10^{3\,314\,360}}}</math>. It was discovered by Daniel Yuan and shared [on Discord](https://discord.com/channels/960643023006490684/1084047886494470185/1254826217375273112) on 24 Jun 2024 and shared on the busy-beaver-discuss email list [the next day](https://groups.google.com/g/busy-beave...")
- 16:19, 9 January 2025 Sligocki talk contribs created page 1RB1LA 1LC0RE 1LF1LD 0RB0LA 1RC1RE ---0LD (Created page with "{{machine|1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD}} {{TM|1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD}} Analysis by @mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1326911501357023296 9 Jan 2025]: <pre> 1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD start: (3,1) (0,2+c) --> (4+c,1) (1,c) --> halt (2+2b,c) --> (7+5b+c,1) (3+2b,c) --> (b,4+b+c) (b,c) := 0^inf <A 1^b 00 1^c 0^inf </pre>")
- 17:29, 10 December 2024 Sligocki talk contribs created page Graham's number (Created page with "'''Graham's number''' (<math>g_{64}</math> or <math>G</math>) is a famously huge number which Martin Gardner claimed was the "largest number ever used in a serious mathematical proof" in 1977. Since it is one of the most famous large numbers, it has become a bit of a yardstick for measuring "hugeness". In the specific context of the Busy Beaver game, we can ask, what is the smallest <math>n</math> such that <math>BB(n) > g_{64}</math>. There is an active search for the s...")
- 16:25, 6 December 2024 Sligocki talk contribs created page 1RB0RC 1RC0LC 0RD1LE 1LE1RF 0LB--- 0RA1LA (Created page with "{{machine|1RB0RC_1RC0LC_0RD1LE_1LE1RF_0LB---_0RA1LA}} {{TM|1RB0RC_1RC0LC_0RD1LE_1LE1RF_0LB---_0RA1LA}} is a holdout BB(6) TM proven infinite by hand by @mxdys on 6 Dec 2024 Analysis by @mxdys: <pre> f(n0, ()) := n0 f(n0, (n,ls)) := 2*(f(n0, ls) - n) start: (2, (), 1) (k, ls, n) --> (k+1, (n,ls), 2*(f(2^k, ls)-(n+2))), f(2^k, ls)-(n+2) >= 0 </pre> Follow up by User:sligocki: <pre> Let (k, ls, n) --> (k+1, [n, ls], n') Then: n'+2 = 2 (f(2^k, ls) - n) - 2...")
- 20:21, 25 November 2024 Sligocki talk contribs created page 1RB1RC 1LC1RE 1LD0LB 1RE1LC 1LE0RF 1RZ1RA (Created page with "{{machine|1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_1RZ1RA}} {{TM|1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_1RZ1RA}} is a long running Halting BB(6) TM analyzed by Racheline on 25 Nov 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1310651468881334394 Discord Link]): Analysis by Racheline: <pre> a_1 = (2^179+1)/3+179 a_2 = (2^a_1+1)/3+a_1 a_3 = (2^a_2+1)/3+a_2 a_4 = (2^a_3+1)/3+a_3-1 a_5 = (2^a_4+1)/3+a_4 the counters after overflow: (10)^17 11 (10)^5...")
- 15:34, 15 November 2024 Sligocki talk contribs created page Talk:Brady's algorithm (Created page with "Hey C7X, what do you think about merging this into the main Tree Normal Form article? My thought is that we could migrate any new content over from here and then turn this into a redirect. IIUC, "Brady's algorithm" is just an alternative name coined by Nick Drozd to describe TNF enumeration. Does that sound right? ~~~~")
- 17:31, 13 November 2024 Sligocki talk contribs created page Transcript (Created page with "A Turing machine '''transcript''' or '''transition history''' is the sequence of transitions that the TM executes when started on a blank tape. Halting TMs have finite transcripts, infinite TMs have infinite transcripts. A finite description of an infinite TM transcript is one way to specify the forward behavior of that TM precisely. Shift rules lead to repeated segments of a TM transcript and vice-versa every repeated segment in a transcript corresponds to a sh...")
- 17:01, 25 September 2024 Sligocki talk contribs created page Hydra function (Created page with "The '''Hydra function''' is Collatz-like function whose behavior is connected to the the unsolved halting problems for the Cryptids Hydra and Antihydra: <math display="block">\begin{array}{l} H(2n) & = & 3n \\ H(2n+1) & = & 3n+1 \\ \end{array}</math> which can alternatively be written as<math display="block">H(n) = \begin{cases} \frac{3n}{2} & \text{if } n \text{ even} \\ \frac{3n-1}{2} & \text{if } n \text{ odd} \\ \end{cases}</math>or...") Tag: Visual edit
- 15:19, 25 September 2024 Sligocki talk contribs created page Lazy Beaver (Created page with "The '''Lazy Beaver''' function is a computable variation of the Busy Beaver function defined by Scott Aaronson in his 2020 review. LB(n, m) is the smallest k such that no n-state, m-symbol Turing machine halts in exactly k steps. == Computed Values == Values found by Terry and Shawn Ligocki in 2021: {| class="wikitable" |+ ! ! ! colspan="5" |States |- ! ! !2 !3 !4 !5 !6 |- | rowspan="5" |Symbols |2 |7 |22 |72 |427 |8,407 |- |3 |23 |351 | | | |- |4...") Tag: Visual edit