1RB1RA 1RC0LC 0LD1LG 1LF0LE 1RZ1LF 0LA1LD 1RA1LC - Revision history

Polygon: Added link to existing user page

2025-10-09T19:27:54Z

Added link to existing user page

← Older revision		Revision as of 19:27, 9 October 2025
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	{{TM\|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC\|halt}} 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.		{{TM\|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC\|halt}} 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:		== Analysis by [[User:Sligocki\|Shawn Ligocki]] ==
	<pre>		<pre>
	1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC		1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC

Polygon: Added Category:BB(7)

2025-09-28T10:04:24Z

Added Category:BB(7)

← Older revision		Revision as of 10:04, 28 September 2025
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	B->A,B,H		B->A,B,H
	</pre>Where here <code>A</code> represents any value = 1,5 (mod 6), <code>B</code> any value = 2,4 (mod 6) and <code>H</code> any value = 3 (mod 6) (which will lead to halt next turn).		</pre>Where here <code>A</code> represents any value = 1,5 (mod 6), <code>B</code> any value = 2,4 (mod 6) and <code>H</code> any value = 3 (mod 6) (which will lead to halt next turn).
			[[Category:BB(7)]]

Polygon: /* Model */ fixed typo

2025-09-14T15:19:54Z

Model: fixed typo

← Older revision		Revision as of 15:19, 14 September 2025
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	== Model ==		== Model ==
	At first it might appear that there is a 1/3 chance of halting each iteration, but in fact, that is not quite right since only ~~they~~ 9k+4 and 9k+5 rules can possibly lead to a halt. Based on manual simulation it appears that the chance of halting each turn reaches a steady state of about 1/7.85. Legion suggested this model: Consider all remainders mod 18 and all the remainders mod 18 that they can lead to:<pre>		At first it might appear that there is a 1/3 chance of halting each iteration, but in fact, that is not quite right since only the 9k+4 and 9k+5 rules can possibly lead to a halt. Based on manual simulation it appears that the chance of halting each turn reaches a steady state of about 1/7.85. Legion suggested this model: Consider all remainders mod 18 and all the remainders mod 18 that they can lead to:<pre>
	0 -> halt		0 -> halt
	1 -> 5,11,17		1 -> 5,11,17

Polygon: Added "halt" to bbch-link

2025-08-16T18:30:55Z

Added "halt" to bbch-link

← Older revision		Revision as of 18:30, 16 August 2025
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	{{machine\|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}		{{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.		{{TM\|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC\|halt}} 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:		Analysis by Shawn Ligocki:

Polygon: Added missing point

2025-08-05T12:36:25Z

Added missing point

← Older revision		Revision as of 12:36, 5 August 2025
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	{{machine\|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}		{{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		{{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:		Analysis by Shawn Ligocki:

Sligocki: Add Model section

2025-05-18T20:43:06Z

Add Model section

← Older revision		Revision as of 20:43, 18 May 2025
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	$ 1^a B> 011^3 --> $ 1^2a+23 B> (for a odd)		$ 1^a B> 011^3 --> $ 1^2a+23 B> (for a odd)
	</pre>		</pre>

			== Model ==
			At first it might appear that there is a 1/3 chance of halting each iteration, but in fact, that is not quite right since only they 9k+4 and 9k+5 rules can possibly lead to a halt. Based on manual simulation it appears that the chance of halting each turn reaches a steady state of about 1/7.85. Legion suggested this model: Consider all remainders mod 18 and all the remainders mod 18 that they can lead to:<pre>
			0 -> halt
			1 -> 5,11,17
			2 -> 1,7,13
			3 -> halt
			4 -> 3,9,15
			5 -> 5,11,17
			6 -> halt
			7 -> 2,8,14
			8 -> 4,10,16
			9 -> halt
			10 -> 1,7,13
			11 -> 5,11,17
			12 -> halt
			13 -> 5,11,17
			14 -> 3,9,15
			15 -> halt
			16 -> 4,10,16
			17 -> 2,8,14
			</pre>(all weights equal) with stationary distribution <code>(0, 1/18(3-sqrt(5)), 1/18(-1+sqrt(5)), 1/18(3-sqrt(5)), 1/18(3-sqrt(5)), 1/9(-1+sqrt(5)), 0, 1/18(3-sqrt(5)), 1/18(-1+sqrt(5)), 1/18(3-sqrt(5)), 1/18(3-sqrt(5)), 1/9(-1+sqrt(5)), 0, 1/18(3-sqrt(5)), 1/18(-1+sqrt(5)), 1/18(3-sqrt(5)), 1/18(3-sqrt(5)), 1/9(-1+sqrt(5)))</code>, halting probability <code>1/6(3-sqrt(5)) ≈ 0.12732</code>, and expected lifetime <code>3/2*(3+sqrt(5)) ≈ 7.8541</code>.


			This model can be simplified to the Markov Chain:<pre>
			A->A,A,B
			B->A,B,H
			</pre>Where here <code>A</code> represents any value = 1,5 (mod 6), <code>B</code> any value = 2,4 (mod 6) and <code>H</code> any value = 3 (mod 6) (which will lead to halt next turn).

Sligocki at 16:12, 17 May 2025

2025-05-17T16:12:37Z

← Older revision		Revision as of 16:12, 17 May 2025
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	D(9k+8) --> D(34 2^k - 18)		D(9k+8) --> D(34 2^k - 18)

	Start: D(5)		Start: D(1)
	</pre>		</pre>

Sligocki: 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:

 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) -..."

2025-05-09T02:40:06Z

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) -..."

New page

{{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) -> Halt(2k+1)

D(9k+1) --> D(32 2^k - 27)
D(9k+4) --> D(32 2^k - 23)
D(9k+7) --> D(32 2^k - 18)

D(9k+2) --> D(34 2^k - 27)
D(9k+5) --> D(34 2^k - 23)
D(9k+8) --> D(34 2^k - 18)

Start: D(5)
</pre>

Basic transitions used to build this:
<pre>
0 1^2n+1 B> 1 --> 1^2n+3 B>
0 1^2n+1 B> 0 1^m 0 --> 1^2n+m+4 B> for m >= 1

0^4 1^2n B> 1 --> 1 B> 010 1^2n 0
0^5 1^2n B> 1 --> 1^5 B> 1^2n 0

0 1^3k B> 00 --> 1 Z> 011^k 00
0^2 1^3k+1 B> 00 --> 1 B> 01 011^k 00
0^3 1^3k+2 B> 00 --> 1 B> 0111 011^k 00

$ 1^a B> 011^3 --> $ 1^2a+23 B> (for a odd)
</pre>