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Added introduction for 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD |
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{{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD|halt}} is a pentational halting [[BB(4,3)]] TM. It was discovered in May 2024 by Pavel Kropitz as one of seven long running TMs. | {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD|halt}} is a pentational halting [[BB(4,3)]] TM. It was discovered in May 2024 by Pavel Kropitz as one of seven long running TMs. | ||
==Analysis== | |||
<pre> | |||
S is any tape configuration | |||
1. S D> 2^a S --> S 2^a D> S [+a steps] | |||
2. S B> 1^a S --> S 1^a B> S [+a steps] | |||
3. S A> 0^2 S --> S <A 1^2 S [+5 steps] | |||
4. S D> (11)^a S --> S (21)^a D> S [+2a steps] | |||
S A> (11)^a S --> S (12)^a A> S [+2a steps] | |||
5. S (21)^a <C S --> S <C (11)^a S [+2a steps] | |||
S (12)^a <A S --> S <A (11)^a S [+2a steps] | |||
6. S (12)^a A> 0^2 S --> S <A (11)^a+1 S [+2a +5 steps] | |||
7. S A> (11)^1 2^b S --> S 2 A> (11)^1 2^b-1 S [+5 steps] | |||
8. S A> (11)^1 2^b S --> S 2^b A> (11)^1 S [+5b steps] | |||
9. S D> 0^2 S --> S <B 2^2 S [+3 steps] | |||
10. S 2 <D (11)^a 0^2 S --> S <D (11)^a+1 2 S [+4a +7 steps] | |||
11. S 2 <D (11)^a 2 0^2 S --> S <D (11)^a+1 2^2 S [+4a +7 steps] | |||
12. S 1^a <A (11)^b 0^2 S --> S 1^a-1 <A (11)^b+1 2 S [+4b +7 steps] | |||
13. S 1^a <A (11)^b 2 0^2 S --> S 1^a-1 <A (11)^b+1 2^2 S [+4b +7 steps] | |||
14. S (12)^a 1 <D (11)^b 0^2 S --> S (12)^a-1 1 <D (11)^b+2 [+4b +8 steps] | |||
15. S (12)^a 1 <D (11)^b 0^inf --> S 1 <D (11)^b+2a 0^inf [+4a^2 +4ba + 4a steps] | |||
16. S (12)^a 2 1 <D (11)^b 0^inf --> S (12)^a-1 2 (12)^b+2 1 <D (11)^1 0^inf [+10b +28 steps] | |||
17. S (12)^a 2 1 <D (11)^b 0^inf --> S (12)^a-1 2 1 <D (11)^2b+5 0^inf | |||
18. S (12)^a 2 1 <D (11)^b 0^inf --> S 2 1 <D (11)^(2^a)*b+(2^a)*5-5 0^inf | |||
19. S (12)^a 2 1 <D (11)^b 2 0^inf --> S (12)^a 2^2 1 <D (11)^2b-1 0^inf | |||
20. S (12)^a 1 <D (11)^b 2 0^inf --> S (12)^a 2 1 <D (11)^2b-1 0^inf | |||
21. S (12)^a 2^2 1 <D (11)^b 0^inf --> S (12)^a-1 2^2 1 <D (11)^2^(b+4)*3-5 0^inf | |||
22. S 1 <D (11)^b 2^2 0^inf --> S 2 (12)^b-1 2 1 <D (11)^1 0^inf | |||
23. S (11)^a 2^2 1 <D (11)^b 0^inf --> S (11)^a-3 (12)^2b+11 2^2 1 <D (11)^1 0^inf | |||
24. 0^inf 2^2 1 <D (11)^c 0^inf --> 0^inf (11)^c+1 (12)^3 2^2 1 <D (11)^1 0^inf | |||
25. 0^inf (11)^2 2^2 1 <D (11)^c 0^inf --> 0^inf 1 (11)^2c+8 (12)^3 2^2 1 <D (11)^1 0^inf | |||
26. 0^inf 1 (11)^1 2^2 1 <D (11)^c 0^inf --> 0^inf 1 (11)^2c+7 (12)^3 2^2 1 <D (11)^1 0^inf | |||
27. 0^inf 1 2^2 1 <D (11)^c 0^inf --> 0^inf (11)^2c+5 (12)^3 2^2 1 <D (11)^1 0^inf | |||
28. 0^inf (11)^1 2^2 1 <D (11)^c 0^inf --> 0^inf 1 Z> 1 (11)^2c+8 0^inf | |||
</pre> | |||
Revision as of 10:24, 5 October 2025
1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD (bbch) is a pentational halting BB(4,3) TM. It was discovered in May 2024 by Pavel Kropitz as one of seven long running TMs.
Analysis
S is any tape configuration 1. S D> 2^a S --> S 2^a D> S [+a steps] 2. S B> 1^a S --> S 1^a B> S [+a steps] 3. S A> 0^2 S --> S <A 1^2 S [+5 steps] 4. S D> (11)^a S --> S (21)^a D> S [+2a steps] S A> (11)^a S --> S (12)^a A> S [+2a steps] 5. S (21)^a <C S --> S <C (11)^a S [+2a steps] S (12)^a <A S --> S <A (11)^a S [+2a steps] 6. S (12)^a A> 0^2 S --> S <A (11)^a+1 S [+2a +5 steps] 7. S A> (11)^1 2^b S --> S 2 A> (11)^1 2^b-1 S [+5 steps] 8. S A> (11)^1 2^b S --> S 2^b A> (11)^1 S [+5b steps] 9. S D> 0^2 S --> S <B 2^2 S [+3 steps] 10. S 2 <D (11)^a 0^2 S --> S <D (11)^a+1 2 S [+4a +7 steps] 11. S 2 <D (11)^a 2 0^2 S --> S <D (11)^a+1 2^2 S [+4a +7 steps] 12. S 1^a <A (11)^b 0^2 S --> S 1^a-1 <A (11)^b+1 2 S [+4b +7 steps] 13. S 1^a <A (11)^b 2 0^2 S --> S 1^a-1 <A (11)^b+1 2^2 S [+4b +7 steps] 14. S (12)^a 1 <D (11)^b 0^2 S --> S (12)^a-1 1 <D (11)^b+2 [+4b +8 steps] 15. S (12)^a 1 <D (11)^b 0^inf --> S 1 <D (11)^b+2a 0^inf [+4a^2 +4ba + 4a steps] 16. S (12)^a 2 1 <D (11)^b 0^inf --> S (12)^a-1 2 (12)^b+2 1 <D (11)^1 0^inf [+10b +28 steps] 17. S (12)^a 2 1 <D (11)^b 0^inf --> S (12)^a-1 2 1 <D (11)^2b+5 0^inf 18. S (12)^a 2 1 <D (11)^b 0^inf --> S 2 1 <D (11)^(2^a)*b+(2^a)*5-5 0^inf 19. S (12)^a 2 1 <D (11)^b 2 0^inf --> S (12)^a 2^2 1 <D (11)^2b-1 0^inf 20. S (12)^a 1 <D (11)^b 2 0^inf --> S (12)^a 2 1 <D (11)^2b-1 0^inf 21. S (12)^a 2^2 1 <D (11)^b 0^inf --> S (12)^a-1 2^2 1 <D (11)^2^(b+4)*3-5 0^inf 22. S 1 <D (11)^b 2^2 0^inf --> S 2 (12)^b-1 2 1 <D (11)^1 0^inf 23. S (11)^a 2^2 1 <D (11)^b 0^inf --> S (11)^a-3 (12)^2b+11 2^2 1 <D (11)^1 0^inf 24. 0^inf 2^2 1 <D (11)^c 0^inf --> 0^inf (11)^c+1 (12)^3 2^2 1 <D (11)^1 0^inf 25. 0^inf (11)^2 2^2 1 <D (11)^c 0^inf --> 0^inf 1 (11)^2c+8 (12)^3 2^2 1 <D (11)^1 0^inf 26. 0^inf 1 (11)^1 2^2 1 <D (11)^c 0^inf --> 0^inf 1 (11)^2c+7 (12)^3 2^2 1 <D (11)^1 0^inf 27. 0^inf 1 2^2 1 <D (11)^c 0^inf --> 0^inf (11)^2c+5 (12)^3 2^2 1 <D (11)^1 0^inf 28. 0^inf (11)^1 2^2 1 <D (11)^c 0^inf --> 0^inf 1 Z> 1 (11)^2c+8 0^inf