BB(2,6): Difference between revisions

Latest revision as of 05:01, 16 September 2026

The 2-state, 6-symbol Busy Beaver problem, BB(2,6), is unsolved. With cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,6).

The current BB(2,6) champion 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) was discovered by Pavel Kropitz in May 2023, proving the lower bound: $S (2, 6) > Σ (2, 6) > 10 ↑ ↑ 10 ↑ ↑ 1 0^{1 0^{115}} > 10 ↑ ↑ ↑ 3$

Top Halters

The scores are given using Knuth's up-arrow notation with an extension to decimal tetration^[1]. The 20 highest known scoring machines are:


TM	Approximate sigma score	Discoverer
`1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA` (bbch)	$10 ↑ ↑ 10 ↑ ↑ 1 0^{1 0^{115}} > 10 ↑ ↑ ↑ 3$	Pavel Kropitz
`1RB2LA1RZ1RB5RB0RB_2LA4RA3LB5LB5RA4LB` (bbch)	10 ↑↑ 19892.08	Peacemaker II
`1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ` (bbch)	10 ↑↑ 91.17	Pavel Kropitz
`1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA` (bbch)	10 ↑↑ 70.27	Shawn Ligocki
`1RB2LB1RZ3LA2LA4RB_1LA3RB4RB1LB5LB0RA` (bbch)	10 ↑↑ 69.68	Shawn Ligocki
`1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ` (bbch)	10 ↑↑ 54.90	Andrew Ducharme
`1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB` (bbch)	10 ↑↑ 42.17	Andrew Ducharme
`1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB` (bbch)	10 ↑↑ 40.07	Andrew Ducharme
`1RB2LA5LB0RA1RA3LB_1LA4LA3LB3RB3RB1RZ` (bbch)	10 ↑↑ 23.9964	Andrew Ducharme
`1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ` (bbch)	10 ↑↑ 21.54	Shawn Ligocki
`1RB2LB3LA1RA0RA1RZ_1LA2RB1LB4RB5RA3LA` (bbch)	10 ↑↑ 20.58	Shawn Ligocki
`1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ` (bbch)	10 ↑↑ 17.53	Shawn Ligocki
`1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ` (bbch)	10 ↑↑ 17.53	Andrew Ducharme
`1RB3RA4LB5RA5LB4RA_2LA1RZ1RB2LA5LA0LA` (bbch)	10 ↑↑ 17.08	Andrew Ducharme
`1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA` (bbch)	10 ↑↑ 15.44	Andrew Ducharme
`1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ2LA` (bbch)	10 ↑↑ 14.35	Andrew Ducharme
`1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ3RA` (bbch)	10 ↑↑ 14.17	Andrew Ducharme
`1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ1LA` (bbch)	10 ↑↑ 14.05	Andrew Ducharme
`1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ0RA` (bbch)	10 ↑↑ 13.69	Andrew Ducharme
`1RB3LA3RA4LB2LB0LA_2LA5LB2RB0RA0RA1RZ` (bbch)	10 ↑↑ 12.42	Andrew Ducharme

All decimal places are truncated.

Phase 1

The initial phase of enumeration and reduction of holdouts took place in November 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated ~24B(illion) TMs of which ~2.278B were holdout TMs. This was reduced to ~22M holdout TMs (a 99.02% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Runtime (hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
Done by	Terry Ligocki	2,278,655,696	$*^{1}$	$*^{2}$	2,109,114,609	7.44%	Description	Data	40.9	1,150.90	15,468.23	Reverse_Engineer_Filter.py	Google Drive
2,109,114,609		683,067,538	67.61%	452.8	874.77	1,293.79	CPS_Filter.py --block-size=1
683,067,538		210,993,434	69.11%	396.4	330.85	478.72	CPS_Filter.py --block-size=2
210,993,434		141,680,232	32.85%	273.9	70.29	213.97	CPS_Filter.py --block-size=3 --max_steps=10_000
141,680,232		66,029,536	53.40%	486.6	43.18	80.87	Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
66,029,536		46,119,004	30.15%	167.4	33.05	109.59	Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
46,119,004		39,034,142	15.36%	170.1	11.57	75.34	CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
39,034,142		29,109,512	25.43%	2,221.6	1.24	4.88	CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
29,109,512		24,536,819	15.71%	384.2	3.31	21.05	Enumerate.py --max-loops=10_000 --block-size=6 --recursive --no-steps --time=0.05 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
24,536,819		22,302,296	9.11%	1,047.5	0.59	6.51	Enumerate.py --max-loops=10_000 --block-size=4 --recursive --no-steps --time=1.00 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000

Phase 2

When Phase 1 was completed, a set of deciders/parameters were run to reduce the number of holdout TMs. The details are given in the various Stages below.

Stage 1

Andrew Ducharme ran another pass of "lr_enum_continue" with the maximum number of steps set to 10 million. The holdouts were reduced from ~22.3M TMs to ~20.4M TMs (a 8.72% reduction). The entry in the table below has a rather technical/arcane/cryptic description. This was an effort to capture enough information to rerun that filter in parallel with specific C++ code, lr_enum_continue, and a specific parallel queuing system, Slurm:

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Runtime (hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
Done by	Andrew Ducharme	22,302,296	$*^{1}$	$*^{2}$	20,358,011	8.72%	Description	Data	1,350.0	0.40	4.59	lr_enum_continue ${WORK_DIR}chunk_${SLURM_ARRAY_TASK_ID} 10000000 ${WORK_DIR}halt_${SLURM_ARRAY_TASK_ID}.txt ${WORK_DIR}inf_${SLURM_ARRAY_TASK_ID}.txt ${WORK_DIR}unknown_${SLURM_ARRAY_TASK_ID}.txt "" false	Google Drive

Stage 2

Starting from the results of Stage 1, Terry Ligocki ran @mxdys' C++ code, "main.exe", using a variety of its deciders with various parameters. A total of 50 variations were run. The holdouts were reduced from ~20.4M TMs to ~907K TMs (a 95.5% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Compute Time (core-hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
Done by	Input	Output	$*^{1}$	$*^{2}$	$*^{3}$	$*^{4}$	Description	Data
Terry Ligocki	20,358,011	19,500,847	4.21%	22.0	10.84	257.42	MitM_CTL RWL_mod sim 1001 maxT 3000 H 6 mod 2 n 6 run	Google Drive
	19,500,847	18,747,861	3.86%	86.0	2.43	63.01	MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 8 run
	18,747,861	4,811,076	74.34%	47.0	82.33	110.75	chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
	4,811,076	2,982,075	38.02%	17.1	29.74	78.22	chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 10000 NG_n 3 run
	2,982,075	2,897,340	2.84%	15.2	1.55	54.64	MitM_CTL RWL_mod sim 1001 maxT 10000 H 8 mod 3 n 6 run
	2,897,340	2,850,781	1.61%	16.7	0.77	48.17	chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 7 run
	2,850,781	2,759,635	3.20%	13.7	1.85	58.01	MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 6 run
	2,759,635	1,953,426	29.21%	13.6	16.48	56.42	chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 30000 NG_n 2 run
	1,953,426	1,855,545	5.01%	2.4	11.18	223.14	MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 3 n 1 run
	1,855,545	1,647,269	11.22%	6.6	8.80	78.40	MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 8 H 1 tH 1 n 4 run
	1,647,269	1,608,166	2.37%	3.4	3.20	134.96	chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2 run
	1,608,166	1,585,745	1.39%	9.6	0.65	46.35	MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n 12 run
	1,585,745	1,555,673	1.90%	5.7	1.47	77.73	chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 10000 NG_n 5 run
	1,555,673	1,428,534	8.17%	9.3	3.78	46.31	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 2 tH 0 n 2 run
	1,428,534	1,340,964	6.13%	0.8	29.70	484.55	chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 10000 NG_n 1 run
	1,340,964	1,286,439	4.07%	0.8	18.40	452.56	chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 3000 NG_n 1 run
	1,286,439	1,273,911	0.97%	0.8	4.20	430.88	chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
	1,273,911	1,265,198	0.68%	0.8	2.88	420.73	chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
	1,265,198	1,258,925	0.50%	0.9	1.99	400.83	chr_LRUH 8 chr_H 6 MitM_CTL NG maxT 30000 NG_n 1 run
	1,258,925	1,242,136	1.33%	0.8	5.51	412.84	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 1 tH 0 n 1 run
	1,242,136	1,231,731	0.84%	1.0	2.78	331.77	MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
	1,231,731	1,216,646	1.22%	1.0	4.15	338.72	MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 2 n 2 run
	1,216,646	1,214,294	0.19%	0.9	0.76	393.03	MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 3 n 1 run
	1,214,294	1,213,431	0.07%	0.9	0.28	391.30	chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 2 run
	1,213,431	1,211,390	0.17%	1.1	0.52	307.13	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 8 H 1 tH 1 n 1 run
	1,211,390	1,209,989	0.12%	1.1	0.35	306.09	chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 4 run
	1,209,989	1,209,974	0.00%	0.9	0.00	381.42	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 1 tH 0 n 1 run
	1,209,974	1,201,890	0.67%	2.5	0.90	134.19	chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2 run
	1,201,890	1,200,086	0.15%	1.3	0.37	248.36	chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 30000 NG_n 1 run
	1,200,086	1,199,734	0.03%	1.2	0.08	270.32	chr_asth 0 chr_LRUH 3 chr_H 3 MitM_CTL NG maxT 100000 NG_n 3 run
	1,199,734	1,198,893	0.07%	2.3	0.10	147.66	MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 6 n 2 run
	1,198,893	1,165,493	2.79%	4.5	2.05	73.44	MitM_CTL RWL_mod sim 1001 maxT 30000 H 4 mod 4 n 1 run
	1,165,493	1,153,863	1.00%	9.3	0.35	34.88	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 0 tH 1 n 4 run
	1,153,863	1,144,711	0.79%	3.7	0.69	87.51	MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 5 n 2 run
	1,144,711	1,127,789	1.48%	7.9	0.60	40.26	chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 30000 NG_n 3 run
	1,127,789	1,124,762	0.27%	4.7	0.18	66.75	MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 8 run
	1,124,762	1,117,226	0.67%	5.6	0.37	55.36	MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 1 n 2 run
	1,117,226	1,109,057	0.73%	7.7	0.30	40.49	chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 100000 NG_n 3 run
	1,109,057	1,083,097	2.34%	11.4	0.63	27.06	chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 30000 NG_n 5 run
	1,083,097	1,077,833	0.49%	11.2	0.13	26.81	chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run
	1,077,833	1,066,795	1.02%	24.1	0.13	12.40	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 6 H 2 tH 1 n 2 run
	1,066,795	1,039,229	2.58%	52.6	0.15	5.64	chr_LRUH 14 chr_H 6 MitM_CTL NG maxT 100000 NG_n 11 run
	1,039,229	1,019,286	1.92%	43.5	0.13	6.63	MitM_CTL RWL_mod sim 1001 maxT 100000 H 12 mod 1 n 3 run
	1,019,286	993,556	2.52%	66.8	0.11	4.24	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 8 H 2 tH 1 n 6 run
	993,556	985,718	0.79%	78.3	0.03	3.53	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 6 H 1 tH 1 n 8 run
	985,718	981,095	0.47%	83.7	0.02	3.27	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 6 H 1 tH 0 n 9 run
	981,095	975,912	0.53%	79.4	0.02	3.43	MitM_CTL RWL_mod sim 1001 maxT 100000 H 16 mod 1 n 8 run
	975,912	974,180	0.18%	84.6	0.01	3.20	MitM_CTL RWL_mod sim 1001 maxT 100000 H 16 mod 4 n 8 run
	974,180	971,254	0.30%	96.9	0.01	2.79	MitM_CTL RWL_mod sim 1001 maxT 100000 H 12 mod 1 n 12 run
	971,254	970,101	0.12%	105.6	0.00	2.56	MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 12 H 0 tH 0 n 18 run

Stage 3

Starting from the results of Stage 2, Andrew Ducharme ran "lr_enum_continue" with the maximum number of steps set to 100 million, then "Enumerate.py" with various parameters. A total of 10 Enumerate variations were run. The holdouts were reduced from ~970K TMs to ~867K TMs (a 10.63% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Compute Time (core-hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Done by	Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
Done by	Input	Output	$*^{1}$	$*^{2}$	$*^{3}$	$*^{4}$	Description	Data
Andrew Ducharme	970,101	939,447	3.16%	--	--	--	lr_enum_continue 100_000_000 steps	Google Drive
	939,447	903,224	3.86%	440.3	0.03	0.59	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=4 --no-ctl --lin-steps=0 --time=2 --force --save-freq=1000
	903,224	895,813	0.82%	647.7	0.00	0.39	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=3 --no-ctl --lin-steps=0 --time=3 --force --save-freq=1000
	895,813	889,838	0.67%	609.3	0.00	0.41	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=8 --no-ctl --lin-steps=0 --time=4 --force --save-freq=1000
	889,838	880,278	1.07%	1,638.9	0.00	0.15	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=12 --no-ctl --lin-steps=0 --force --save-freq=1000
	880,278	877,485	0.32%	1,885.5	0.00	0.13	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=6 --no-ctl --lin-steps=0 --force --save-freq=1000
	877,485	875,062	0.28%	2,068.8	0.00	0.12	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=5 --no-ctl --lin-steps=0 --force --save-freq=1000
	875,062	873,469	0.18%	1,785.4	0.00	0.14	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=7 --no-ctl --lin-steps=0 --force --save-freq=1000
	873,469	870,085	0.39%	9,270.0	0.00	0.03	Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=2 --tape-limit=500 --time=120 --no-ctl --lin-steps=0 --force --save-freq=1000
	870,085	869,001	0.12%	4,498.3	0.00	0.05	Enumerate.py --no-steps --exp-linear-rules --max_loops=10_000_000 --block-mult=60 --tape-limit=5000 --no-ctl --lin-steps=0 --force --save-freq=1000
	869,001	867,008	0.23%	3997.4	0.00	0.06	Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=9 --tape-limit=5000 --max-steps-per-macro=100_000 --lin-steps=0 --no-ctl --force --save-freq=250

The total time spent on the lr_enum_continue computation was not recorded.

Stage 4

Following the release of @mxdys's implementation of FAR deciders in C++, these deciders were applied to the 2x6 holdouts by Andrew Ducharme. The details are given in this table, including links to the Google Drive with the holdouts and solved TMs per decider:

(done to reduce column size: $*^{1}$ = % Reduced, $*^{2}$ = Compute Time (core-hours), $*^{3}$ = Decided, $*^{4}$ = Processed)

Holdout TMs		$*^{1}$	$*^{2}$	TMs/sec/core		Description	Data
Input	Output	$*^{1}$	$*^{2}$	$*^{3}$	$*^{4}$	Description	Data
867,008	811,301	6.43%	0.043	364.10	5,666.72	FAR CPS_LRU maxT 100000 LRUH 2 H 1 tH 1 n 2	Google Drive
811,301	806,119	0.64%	0.159	9.03	1,413.42	FAR CPS_LRU maxT 100000 LRUH 3 H 1 tH 1 n 2
806,119	736,690	8.61%	0.548	35.21	408.78	FAR CPS_LRU maxT 100000 LRUH 4 H 1 tH 1 n 2
736,690	736,504	0.03%	0.009	5.81	23,021.56	FAR CPS_LRU maxT 100000 LRUH 1 H 1 tH 1 n 1
736,504	735,317	0.16%	0.058	5.71	3,540.88	FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2
735,317	733,717	0.22%	0.341	1.30	599.28	FAR CPS_LRU maxT 100000 LRUH 4 H 2 tH 2 n 2
733,717	673,920	8.15%	3.8	4.43	54.32	FAR CPS_LRU maxT 100000 LRUH 4 H 2 tH 2 n 4
673,920	652,828	3.13%	~10	---	---	FAR CPS_LRU maxT 100000 LRUH 6 H 2 tH 2 n 4
652,828	645,264	1.16%	~12	---	---	FAR CPS_LRU maxT 100000 LRUH 8 H 2 tH 2 n 4
645,264	641,388	0.60%	~15	---	---	FAR CPS_LRU maxT 100000 LRUH 10 H 2 tH 2 n 10
641,388	635,505	0.92%	~200	---	---	FAR CPS_LRU maxT 1000000 LRUH 10 H 1 tH 2 n 10
635,505	616,639	2.97%	---	---	---	FAR CPS_LRU maxT 1000000 LRUH 2 H 0 tH 0 n [3-10]
616,639	592,039	3.99%	~700	---	---	FAR CPS_LRU maxT 1000000 LRUH 3 H 0 tH 0 n [1-10]
592,039	576,938	2.55%	~800	---	---	FAR CPS_LRU maxT 1000000 LRUH 3 H [0-1] tH [0-1] n [1-10]
576,938	572,963	0.69%	~1,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 4 H 0 tH 0 n [1-10]
572,963	567,971	0.87%	~1,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 4 H 2 tH 0 n [1-10]
567,971	566,096	0.33%	~1,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 6 H 0 tH 0 n [1-10]
566,096	564,290	0.32%	~1,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 8 H 0 tH [0,2] n [1-10]
564,290	559,553	0.84%	~1,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 8 H 2 tH 1 n [1-10]
559,553	558,039	0.27%	~900	---	---	FAR CPS_LRU maxT 1000000 LRUH 8 H 2 tH 2 n [1-10]
558,039	556,814	0.22%	~14,000	---	---	FAR CPS_LRU maxT 1000000 LRUH [12,16] H [0-2] tH [0-2] n [1-10]
556,814	554,479	0.42%	~3,600	---	---	FAR CPS_LRU maxT 1000000 LRUH [1-3]
554,479	551,586	0.52%	~5000	---	---	FAR CPS_LRU maxT 1000000 LRUH 4
551,586	548,993	0.47%	~13,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 5
548,993	545,005	0.73%	~57,000	---	---	FAR CPS_LRU maxT 1000000 LRUH 6 and 8
545,005	542,325	0.49%	6851.2	0.00	0.022	Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=96 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
542,325	537,393	0.91%	9032.1	0.00	0.017	Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=2 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
537,393	536,112	0.24%	8969.4	0.00	0.017	Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=3 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
536,112	533,764	0.43%	8778.5	---	---	Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=7 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
533,764	527,232	1.22%	~3500	---	---	chr_LRUH 1 chr_H 0 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 2 chr_H 1 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 3 chr_H 2 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 5 chr_H 4 MitM_CTL NG maxT 1 s NG_n [1-15] chr_LRUH 7 chr_H 6 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 9 chr_H 8 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 11 chr_H 8 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 12 chr_H 10 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 13 chr_H 12 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 1 s NG_n [1-10] chr_LRUH 15 chr_H 12 MitM_CTL NG maxT 1 s NG_n [1-10]
527,232	502,532	4.68%	4.1	---	---	Inductive_inf.v --maxT 1000 --arithseq --exploop
502,532	501,914	0.12%	~1700	---	---	chr_LRUH [8,10,12,16] chr_H [chr_LRUH-4] MitM_CTL NG maxT 1 s NG_n [1-10]
501,914	439,120	12.51%	42.87	---	---	Inductive_inf.v --maxT 10000 --exploop
439,120	437,729	0.32%	~2000	---	---	FAR RWL_mod maxT 1000000 H [1-2] mod [1-6] n [1-10]
437,729	432,360	1.23%	~2800	---	---	FAR RWL_mod maxT 1000000 H [3] mod [1-6] n [1-10]
432,360	424,733	1.76%	~3200	---	---	FAR RWL_mod maxT 1000000 H [4] mod [1-6] n [1-10]
424,733	419,045	1.34%	~450	---	---	FAR RWL_mod maxT 100000 H [6] mod [1-6] n [1-10]
419,045	418,127	0.22%	~600	---	---	FAR RWL_mod maxT 100000 H [8] mod [1-6] n [1-10]
418,127	416,677	0.35%	~2800	---	---	chr_LRUH 12 chr_H 6 MitM_CTL NG maxT 1000000 NG_n [1-10] chr_LRUH 13 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10] chr_LRUH 14 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10] chr_LRUH 15 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10] chr_LRUH 16 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10]
416,677	415,414	0.30%	~4300	---	---	chr_LRUH [17-22] chr_H 12 MitM_CTL NG maxT 1000000 NG_n [1-10]
415,414	414,009	0.34%	~6600	---	---	chr_asth 0 chr_LRUH [x] chr_H [x] MitM_CTL NG maxT 1000000 NG_n [1-16], x=[8,12,16,24,32]
414,009	413,513	0.12%	?	---	---	chr_LRUH [2-6,8,12,14,16,28] chr_LRUn 2 MitM_CTL NG maxT 1000000 NG_n [1-4,6,8,12,16]
413,513	413,207	0.07%	?	---	---	chr_LRUH [3,7,12,14,16,20,28] chr_LRUn 3 MitM_CTL NG maxT 1000000 NG_n [1-4,6,8,12,16]
413,207	412,086	0.27%	?	---	---	FAR RWL_mod maxT 1000000 H 5 mod [1-6] n [1-10]

References

↑ Shawn Ligocki. 2022. "Extending Up-arrow Notation"

[1] Shawn Ligocki. 2022. "Extending Up-arrow Notation"

[1]

BB(2,6): Difference between revisions

Latest revision as of 05:01, 16 September 2026

Contents

Top Halters

Phase 1

Phase 2

Stage 1

Stage 2

Stage 3

Stage 4

References

Navigation menu

@@ Line 12: / Line 12: @@
 |-
 |{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
-|10 ↑↑↑ 3
+|<math>10 \uparrow \uparrow 10 \uparrow\uparrow 10^{10^{115}} > 10 \uparrow \uparrow \uparrow 3</math>
 |Pavel Kropitz
 |-
@@ Line 41: / Line 41: @@
 |{{TM|1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB|halt}}
 |10 ↑↑ 40.07
+|Andrew Ducharme
+|-
+|{{TM|1RB2LA5LB0RA1RA3LB_1LA4LA3LB3RB3RB1RZ|halt}}
+|10 ↑↑ 23.9964
 |Andrew Ducharme
 |-
@@ Line 85: / Line 89: @@
 |{{TM|1RB3LA3RA4LB2LB0LA_2LA5LB2RB0RA0RA1RZ|halt}}
 |10 ↑↑ 12.42
-|Andrew Ducharme
-|-
-|{{TM|1RB0LB4LA2RA2RB1LB_2LA4LA3LB5LA1RA1RZ|halt}}
-|10 ↑↑ 11.70
 |Andrew Ducharme
 |}
@@ Line 94: / Line 94: @@
 == Phase 1 ==
-The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated ~24B(illion) TMs of which ~2,278B were holdout TMs. This was reduced to ~22M holdout TMs (a 99.02% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:
+The initial phase of enumeration and reduction of [[holdouts]] took place in November 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated ~24B(illion) TMs of which ~2.278B were holdout TMs. This was reduced to ~22M holdout TMs (a 99.02% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:
 (done to reduce column size:
@@ Line 111: / Line 111: @@
 !rowspan="2" |Data
 |-
-|style="text-align:left" |Terry Ligocki
+|style="text-align:center" rowspan="100" |Terry Ligocki
 |2,278,655,696
 |2,109,114,609
@@ Line 119: / Line 119: @@
 |15,468.23
 |style="text-align:left" |Reverse_Engineer_Filter.py
-|style="text-align:left", rowspan="100" |[https://drive.google.com/drive/folders/1p9b5g-Id3WEMUYIwEnaKWRBGIW66ADjM?usp=drive_link Google Drive]
+|style="text-align:center" rowspan="100" |[https://drive.google.com/drive/folders/1p9b5g-Id3WEMUYIwEnaKWRBGIW66ADjM?usp=drive_link Google Drive]
 |-
-|style="text-align:left" |Terry Ligocki
 |2,109,114,609
 |683,067,538
@@ Line 130: / Line 129: @@
 |style="text-align:left" |CPS_Filter.py --block-size=1
 |-
-|style="text-align:left" |Terry Ligocki
 |683,067,538
 |210,993,434
@@ Line 139: / Line 137: @@
 |style="text-align:left" |CPS_Filter.py --block-size=2
 |-
-|style="text-align:left" |Terry Ligocki
 |210,993,434
 |141,680,232
@@ Line 148: / Line 145: @@
 |style="text-align:left" |CPS_Filter.py --block-size=3 --max_steps=10_000
 |-
-|style="text-align:left" |Terry Ligocki
 |141,680,232
 |66,029,536
@@ Line 157: / Line 153: @@
 |style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
 |-
-|style="text-align:left" |Terry Ligocki
 |66,029,536
 |46,119,004
@@ Line 166: / Line 161: @@
 |style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
 |-
-|style="text-align:left" |Terry Ligocki
 |46,119,004
 |39,034,142
@@ Line 175: / Line 169: @@
 |style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
 |-
-|style="text-align:left" |Terry Ligocki
 |39,034,142
 |29,109,512
@@ Line 184: / Line 177: @@
 |style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
 |-
-|style="text-align:left" |Terry Ligocki
 |29,109,512
 |24,536,819
@@ Line 193: / Line 185: @@
 |style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=6 --recursive --no-steps --time=0.05 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
 |-
-|style="text-align:left" |Terry Ligocki
 |24,536,819
 |22,302,296
@@ Line 258: / Line 249: @@
 !<math>*^4</math>
 |-
-|style="text-align:left" |Terry Ligocki
+|style="text-align:left" rowspan="50"|Terry Ligocki
 |20,358,011
 |19,500,847
@@ Line 268: / Line 259: @@
 |style="text-align:left" rowspan="50"|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT?usp=drive_link Google Drive]
 |-
-|style="text-align:left" |Terry Ligocki
 |19,500,847
 |18,747,861
@@ Line 277: / Line 267: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 8 run
 |-
-|style="text-align:left" |Terry Ligocki
 |18,747,861
 |4,811,076
@@ Line 286: / Line 275: @@
 |style="text-align:left" |chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
 |-
-|style="text-align:left" |Terry Ligocki
 |4,811,076
 |2,982,075
@@ Line 295: / Line 283: @@
 |style="text-align:left" |chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 10000 NG_n 3 run
 |-
-|style="text-align:left" |Terry Ligocki
 |2,982,075
 |2,897,340
@@ Line 304: / Line 291: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 8 mod 3 n 6 run
 |-
-|style="text-align:left" |Terry Ligocki
 |2,897,340
 |2,850,781
@@ Line 313: / Line 299: @@
 |style="text-align:left" |chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 7 run
 |-
-|style="text-align:left" |Terry Ligocki
 |2,850,781
 |2,759,635
@@ Line 322: / Line 307: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 6 run
 |-
-|style="text-align:left" |Terry Ligocki
 |2,759,635
 |1,953,426
@@ Line 331: / Line 315: @@
 |style="text-align:left" |chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 30000 NG_n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,953,426
 |1,855,545
@@ Line 340: / Line 323: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 3 n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,855,545
 |1,647,269
@@ Line 349: / Line 331: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 8 H 1 tH 1 n 4 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,647,269
 |1,608,166
@@ Line 358: / Line 339: @@
 |style="text-align:left" |chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,608,166
 |1,585,745
@@ Line 367: / Line 347: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n 12 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,585,745
 |1,555,673
@@ Line 376: / Line 355: @@
 |style="text-align:left" |chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 10000 NG_n 5 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,555,673
 |1,428,534
@@ Line 385: / Line 363: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 2 tH 0 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,428,534
 |1,340,964
@@ Line 394: / Line 371: @@
 |style="text-align:left" |chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 10000 NG_n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,340,964
 |1,286,439
@@ Line 403: / Line 379: @@
 |style="text-align:left" |chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 3000 NG_n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,286,439
 |1,273,911
@@ Line 412: / Line 387: @@
 |style="text-align:left" |chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,273,911
 |1,265,198
@@ Line 421: / Line 395: @@
 |style="text-align:left" |chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,265,198
 |1,258,925
@@ Line 430: / Line 403: @@
 |style="text-align:left" |chr_LRUH 8 chr_H 6 MitM_CTL NG maxT 30000 NG_n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,258,925
 |1,242,136
@@ Line 439: / Line 411: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 1 tH 0 n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,242,136
 |1,231,731
@@ Line 448: / Line 419: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,231,731
 |1,216,646
@@ Line 457: / Line 427: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 2 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,216,646
 |1,214,294
@@ Line 466: / Line 435: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 3 n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,214,294
 |1,213,431
@@ Line 475: / Line 443: @@
 |style="text-align:left" |chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,213,431
 |1,211,390
@@ Line 484: / Line 451: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 8 H 1 tH 1 n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,211,390
 |1,209,989
@@ Line 493: / Line 459: @@
 |style="text-align:left" |chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 4 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,209,989
 |1,209,974
@@ Line 502: / Line 467: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 1 tH 0 n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,209,974
 |1,201,890
@@ Line 511: / Line 475: @@
 |style="text-align:left" |chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,201,890
 |1,200,086
@@ Line 520: / Line 483: @@
 |style="text-align:left" |chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 30000 NG_n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,200,086
 |1,199,734
@@ Line 529: / Line 491: @@
 |style="text-align:left" |chr_asth 0 chr_LRUH 3 chr_H 3 MitM_CTL NG maxT 100000 NG_n 3 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,199,734
 |1,198,893
@@ Line 538: / Line 499: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 6 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,198,893
 |1,165,493
@@ Line 547: / Line 507: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 30000 H 4 mod 4 n 1 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,165,493
 |1,153,863
@@ Line 556: / Line 515: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 0 tH 1 n 4 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,153,863
 |1,144,711
@@ Line 565: / Line 523: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 5 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,144,711
 |1,127,789
@@ Line 574: / Line 531: @@
 |style="text-align:left" |chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 30000 NG_n 3 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,127,789
 |1,124,762
@@ Line 583: / Line 539: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 8 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,124,762
 |1,117,226
@@ Line 592: / Line 547: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 1 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,117,226
 |1,109,057
@@ Line 601: / Line 555: @@
 |style="text-align:left" |chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 100000 NG_n 3 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,109,057
 |1,083,097
@@ Line 610: / Line 563: @@
 |style="text-align:left" |chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 30000 NG_n 5 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,083,097
 |1,077,833
@@ Line 619: / Line 571: @@
 |style="text-align:left" |chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,077,833
 |1,066,795
@@ Line 628: / Line 579: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 6 H 2 tH 1 n 2 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,066,795
 |1,039,229
@@ Line 637: / Line 587: @@
 |style="text-align:left" |chr_LRUH 14 chr_H 6 MitM_CTL NG maxT 100000 NG_n 11 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,039,229
 |1,019,286
@@ Line 646: / Line 595: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 12 mod 1 n 3 run
 |-
-|style="text-align:left" |Terry Ligocki
 |1,019,286
 |993,556
@@ Line 655: / Line 603: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 8 H 2 tH 1 n 6 run
 |-
-|style="text-align:left" |Terry Ligocki
 |993,556
 |985,718
@@ Line 664: / Line 611: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 6 H 1 tH 1 n 8 run
 |-
-|style="text-align:left" |Terry Ligocki
 |985,718
 |981,095
@@ Line 673: / Line 619: @@
 |style="text-align:left" |MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 6 H 1 tH 0 n 9 run
 |-
-|style="text-align:left" |Terry Ligocki
 |981,095
 |975,912
@@ Line 682: / Line 627: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 16 mod 1 n 8 run
 |-
-|style="text-align:left" |Terry Ligocki
 |975,912
 |974,180
@@ Line 691: / Line 635: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 16 mod 4 n 8 run
 |-
-|style="text-align:left" |Terry Ligocki
 |974,180
 |971,254
@@ Line 700: / Line 643: @@
 |style="text-align:left" |MitM_CTL RWL_mod sim 1001 maxT 100000 H 12 mod 1 n 12 run
 |-
-|style="text-align:left" |Terry Ligocki
 |971,254
 |970,101
@@ Line 711: / Line 653: @@
 === Stage 3 ===
-Starting from the results of Stage 2, Andrew Ducharme ran  "lr_enum_continue" with the maximum number of steps set to 100 million, then "Enumerate.py" with various parameters. A total of 6 Enumerate variations were run. The holdouts were reduced from ~970K TMs to ~870K TMs (a 10.31% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:
+Starting from the results of Stage 2, Andrew Ducharme ran  "lr_enum_continue" with the maximum number of steps set to 100 million, then "Enumerate.py" with various parameters. A total of 10 Enumerate variations were run. The holdouts were reduced from ~970K TMs to ~867K TMs (a 10.63% reduction). The details are given in this table, including links to the Google Drive with the holdouts and details of the computation:
 (done to reduce column size:
@@ Line 733: / Line 675: @@
 !<math>*^4</math>
 |-
-|Andrew Ducharme
+|style="text-align:center" rowspan="11" |Andrew Ducharme
 |970,101
 |939,447
@@ Line 740: / Line 682: @@
 | --
 | --
-|lr_enum_continue 100_000_000 steps
+|style="text-align:left" |lr_enum_continue 100_000_000 steps
-| rowspan="7" |[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT?usp=drive_link Google Drive]
+|style="text-align:center" rowspan="11" |[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT?usp=drive_link Google Drive]
+|-
+|939,447
+|903,224
+|3.86%
+|440.3
+|0.03
+|0.59
+|style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=4 --no-ctl --lin-steps=0 --time=2  --force --save-freq=1000
+|-
+|903,224
+|895,813
+|0.82%
+|647.7
+|0.00
+|0.39
+|style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=3 --no-ctl --lin-steps=0 --time=3  --force --save-freq=1000
 |-
-| style="text-align:left" |Andrew Ducharme
 |895,813
 |889,838
@@ Line 752: / Line 709: @@
 | style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=8 --no-ctl --lin-steps=0 --time=4  --force --save-freq=1000
 |-
-|style="text-align:left" |Andrew Ducharme
 |889,838
 |880,278
@@ Line 761: / Line 717: @@
 |style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=12 --no-ctl --lin-steps=0  --force --save-freq=1000
 |-
-|style="text-align:left" |Andrew Ducharme
 |880,278
 |877,485
@@ Line 770: / Line 725: @@
 |style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=6 --no-ctl --lin-steps=0  --force --save-freq=1000
 |-
-|style="text-align:left" |Andrew Ducharme
 |877,485
 |875,062
@@ Line 779: / Line 733: @@
 |style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=5 --no-ctl --lin-steps=0  --force --save-freq=1000
 |-
-|style="text-align:left" |Andrew Ducharme
 |875,062
 |873,469
@@ Line 788: / Line 741: @@
 |style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=7 --no-ctl --lin-steps=0  --force --save-freq=1000
 |-
-|style="text-align:left" |Andrew Ducharme
 |873,469
 |870,085
@@ Line 796: / Line 748: @@
 |0.03
 |style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=1_000_000 --block-mult=2 --tape-limit=500 --time=120 --no-ctl --lin-steps=0  --force --save-freq=1000
+|-
+|870,085
+|869,001
+|0.12%
+|4,498.3
+|0.00
+|0.05
+|style="text-align:left" |Enumerate.py --no-steps --exp-linear-rules --max_loops=10_000_000 --block-mult=60 --tape-limit=5000 --no-ctl --lin-steps=0  --force --save-freq=1000
+|-
+|869,001
+|867,008
+|0.23%
+|3997.4
+|0.00
+|0.06
+|style="text-align:left"|Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=9 --tape-limit=5000 --max-steps-per-macro=100_000 --lin-steps=0 --no-ctl --force --save-freq=250
+|}
+The total time spent on the lr_enum_continue computation was not recorded.
+=== Stage 4 ===
+Following the release of @mxdys's implementation of FAR deciders in C++, these deciders were applied to the 2x6 holdouts by Andrew Ducharme. The details are given in this table, including links to the Google Drive with the holdouts and solved TMs per decider:
+(done to reduce column size:
+<math>*^1</math>= % Reduced,
+<math>*^2</math>= Compute Time (core-hours),
+<math>*^3</math>= Decided,
+<math>*^4</math>= Processed)
+{| class="wikitable sortable" style="text-align: right"
+! colspan="2" |Holdout TMs
+! rowspan="2" |<math>*^1</math>
+! rowspan="2" |<math>*^2</math>
+! colspan="2" |TMs/sec/core
+! rowspan="2" |Description
+! rowspan="2" |Data
+|-
+!Input
+!Output
+!<math>*^3</math>
+!<math>*^4</math>
+|-
+|867,008
+|811,301
+|6.43%
+|0.043
+|364.10
+|5,666.72
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 2 H 1 tH 1 n 2
+|style="text-align:center" rowspan="44" |[https://drive.google.com/drive/folders/18njhmOzRc67zCmVuLd0aDxl6ETBhL1gy?usp=sharing Google Drive]
+|-
+|811,301
+|806,119
+|0.64%
+|0.159
+|9.03
+|1,413.42
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 3 H 1 tH 1 n 2
+|-
+|806,119
+|736,690
+|8.61%
+|0.548
+|35.21
+|408.78
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 4 H 1 tH 1 n 2
+|-
+|736,690
+|736,504
+|0.03%
+|0.009
+|5.81
+|23,021.56
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 1 H 1 tH 1 n 1
+|-
+|736,504
+|735,317
+|0.16%
+|0.058
+|5.71
+|3,540.88
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2
+|-
+|735,317
+|733,717
+|0.22%
+|0.341
+|1.30
+|599.28
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 4 H 2 tH 2 n 2
+|-
+|733,717
+|673,920
+|8.15%
+|3.8
+|4.43
+|54.32
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 4 H 2 tH 2 n 4
+|-
+|673,920
+|652,828
+|3.13%
+|~10
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 6 H 2 tH 2 n 4
+|-
+|652,828
+|645,264
+|1.16%
+|~12
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 8 H 2 tH 2 n 4
+|-
+|645,264
+|641,388
+|0.60%
+|~15
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 100000 LRUH 10 H 2 tH 2 n 10
+|-
+|641,388
+|635,505
+|0.92%
+|~200
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 10 H 1 tH 2 n 10
+|-
+|635,505
+|616,639
+|2.97%
+| ---
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 2 H 0 tH 0 n [3-10]
+|-
+|616,639
+|592,039
+|3.99%
+|~700
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 3 H 0 tH 0 n [1-10]
+|-
+|592,039
+|576,938
+|2.55%
+|~800
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 3 H [0-1] tH [0-1] n [1-10]
+|-
+|576,938
+|572,963
+|0.69%
+|~1,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 4 H 0 tH 0 n [1-10]
+|-
+|572,963
+|567,971
+|0.87%
+|~1,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 4 H 2 tH 0 n [1-10]
+|-
+|567,971
+|566,096
+|0.33%
+|~1,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 6 H 0 tH 0 n [1-10]
+|-
+|566,096
+|564,290
+|0.32%
+|~1,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 8 H 0 tH [0,2] n [1-10]
+|-
+|564,290
+|559,553
+|0.84%
+|~1,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 8 H 2 tH 1 n [1-10]
+|-
+|559,553
+|558,039
+|0.27%
+|~900
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 8 H 2 tH 2 n [1-10]
+|-
+|558,039
+|556,814
+|0.22%
+|~14,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH [12,16] H [0-2] tH [0-2] n [1-10]
+|-
+|556,814
+|554,479
+|0.42%
+|~3,600
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH [1-3]
+|-
+|554,479
+|551,586
+|0.52%
+|~5000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 4
+|-
+|551,586
+|548,993
+|0.47%
+|~13,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 5
+|-
+|548,993
+|545,005
+|0.73%
+|~57,000
+| ---
+| ---
+|style="text-align:left" |FAR CPS_LRU maxT 1000000 LRUH 6 and 8
+|-
+|545,005
+|542,325
+|0.49%
+|6851.2
+|0.00
+|0.022
+|style="text-align:left" |Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=96 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
+|-
+|542,325
+|537,393
+|0.91%
+|9032.1
+|0.00
+|0.017
+|style="text-align:left" |Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=2 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
+|-
+|537,393
+|536,112
+|0.24%
+|8969.4
+|0.00
+|0.017
+|style="text-align:left" |Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=3 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
+|-
+|536,112
+|533,764
+|0.43%
+|8778.5
+| ---
+| ---
+|style="text-align:left" |Enumerate.py -r --no-steps --exp-linear-rules --max-loops=100_000_000 --block-mult=7 --tape-limit=50_000 --max-steps-per-macro=1_000_000 --time=60 --lin-steps=0 --no-ctl
+|-
+|533,764
+|527,232
+|1.22%
+|~3500
+| ---
+| ---
+|style="text-align:left" |
+chr_LRUH 1 chr_H 0 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 2 chr_H 1 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 3 chr_H 2 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 5 chr_H 4 MitM_CTL NG maxT 1 s NG_n [1-15]
+chr_LRUH 7 chr_H 6 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 9 chr_H 8 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 11 chr_H 8 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 12 chr_H 10 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 13 chr_H 12 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 1 s NG_n [1-10]
+chr_LRUH 15 chr_H 12 MitM_CTL NG maxT 1 s NG_n [1-10]
+|-
+|527,232
+|502,532
+|4.68%
+|4.1
+| ---
+| ---
+|style="text-align:left" |Inductive_inf.v --maxT 1000 --arithseq --exploop
+|-
+|502,532
+|501,914
+|0.12%
+|~1700
+| ---
+| ---
+|style="text-align:left" |chr_LRUH [8,10,12,16] chr_H [chr_LRUH-4] MitM_CTL NG maxT 1 s NG_n [1-10]
+|-
+|501,914
+|439,120
+|12.51%
+|42.87
+| ---
+| ---
+|style="text-align:left" |Inductive_inf.v --maxT 10000 --exploop
+|-
+|439,120
+|437,729
+|0.32%
+|~2000
+| ---
+| ---
+|style="text-align:left" |FAR RWL_mod maxT 1000000 H [1-2] mod [1-6] n [1-10]
+|-
+|437,729
+|432,360
+|1.23%
+|~2800
+| ---
+| ---
+|style="text-align:left" |FAR RWL_mod maxT 1000000 H [3] mod [1-6] n [1-10]
+|-
+|432,360
+|424,733
+|1.76%
+|~3200
+| ---
+| ---
+|style="text-align:left" |FAR RWL_mod maxT 1000000 H [4] mod [1-6] n [1-10]
+|-
+|424,733
+|419,045
+|1.34%
+|~450
+| ---
+| ---
+|style="text-align:left" |FAR RWL_mod maxT 100000 H [6] mod [1-6] n [1-10]
+|-
+|419,045
+|418,127
+|0.22%
+|~600
+| ---
+| ---
+|style="text-align:left" |FAR RWL_mod maxT 100000 H [8] mod [1-6] n [1-10]
+|-
+|418,127
+|416,677
+|0.35%
+|~2800
+| ---
+| ---
+|style="text-align:left" |
+chr_LRUH 12 chr_H 6 MitM_CTL NG maxT 1000000 NG_n [1-10]
+chr_LRUH 13 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10]
+chr_LRUH 14 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10]
+chr_LRUH 15 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10]
+chr_LRUH 16 chr_H 8 MitM_CTL NG maxT 1000000 NG_n [1-10]
+|-
+|416,677
+|415,414
+|0.30%
+|~4300
+| ---
+| ---
+|style="text-align:left" |chr_LRUH [17-22] chr_H 12 MitM_CTL NG maxT 1000000 NG_n [1-10]
+|-
+|415,414
+|414,009
+|0.34%
+|~6600
+| ---
+| ---
+|style="text-align:left" |chr_asth 0 chr_LRUH [x] chr_H [x] MitM_CTL NG maxT 1000000 NG_n [1-16], x=[8,12,16,24,32]
+|-
+|414,009
+|413,513
+|0.12%
+| ?
+| ---
+| ---
+|style="text-align:left" |chr_LRUH [2-6,8,12,14,16,28] chr_LRUn 2 MitM_CTL NG maxT 1000000 NG_n [1-4,6,8,12,16]
+|-
+|413,513
+|413,207
+|0.07%
+| ?
+| ---
+| ---
+|style="text-align:left" |chr_LRUH [3,7,12,14,16,20,28] chr_LRUn 3 MitM_CTL NG maxT 1000000 NG_n [1-4,6,8,12,16]
+|-
+|413,207
+|412,086
+|0.27%
+| ?
+| ---
+| ---
+|style="text-align:left" |FAR RWL_mod maxT 1000000 H 5 mod [1-6] n [1-10]
 |}
-The total time spent on the lr_enum_continue computation was not recorded.
-==References==
+== References ==
 <!--
 A far more efficient pipeline would immediately apply lr_enum_continue out to 1M steps to Terry Ligocki's holdout list. lr_enum_continue, written in C++, is about 400x faster than Enumerate.py at checking for Lin Recursion. Using Enumerate.py meant its Reverse Engineering decider was applied to all holdouts, and solved 74,089 TMs (0.33% of holdouts)...at the cost of roughly 274.1 hours of compute.
 -->
-[[Category: BB Domains]]
+[[Category: BB Domains]][[Category:BB(2,6)]]

BB(2,6): Difference between revisions

Latest revision as of 05:01, 16 September 2026

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