BB(2,4): Difference between revisions
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BB(2,4) was unofficially found to be 3,932,964 on April 10, 2023 by the bbchallenge project, when deciders made for solving BB(5) eliminated the last BB(2,4) holdouts. The champion machine M, with S(M) = 3,932,964 and Σ(M) = 2,050, was found by Terry and Shawn Ligocki in February 2005. | BB(2,4) was unofficially found to be 3,932,964 on April 10, 2023 by the bbchallenge project, when deciders made for solving BB(5) eliminated the last BB(2,4) holdouts. The champion machine M, with S(M) = 3,932,964 and Σ(M) = 2,050, was found by Terry and [[User:sligocki|Shawn Ligocki]] in February 2005. | ||
Work formalizing this result is ongoing. | Work formalizing this result is ongoing. | ||
== History == | == History == | ||
Brady found a steps and ones champion in 1988, establishing S(2,4) ≥ 7195 and Σ(2,4) ≥ 90.<ref>Brady A.H. (1988) The busy beaver game and the meaning of life in: The Universal Turing Machine: A Half-Century Survey, R. Herken (Ed.), Oxford University Press, 1988, 259-277.</ref> | * Brady found a steps and ones champion in 1988, establishing S(2,4) ≥ 7195 and Σ(2,4) ≥ 90.<ref>Brady A.H. (1988) The busy beaver game and the meaning of life in: The Universal Turing Machine: A Half-Century Survey, R. Herken (Ed.), Oxford University Press, 1988, 259-277.</ref> | ||
* Terry and Shawn Ligocki found the current champion in 2005. | |||
== | == Champion == | ||
S(2,4) = 3,932,964 and | S(2,4) = 3,932,964 and Σ(2,4) = 2050 and both are achieved by only one champion (in [[TNF]]): | ||
* {{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}} | |||
* {{TM| | |||
== Enumeration == | == Enumeration == | ||
The top longest running BB(2,4) TMs (in [[TNF-1RB]]) are: | The top 20 longest running BB(2,4) TMs (in [[TNF-1RB]]) are: | ||
Standard Format Steps Σ | Standard Format Steps Σ | ||
1RB2LA1RA1RA_1LB1LA3RB1RZ Halt 3932964 2050 | |||
1RB3LA1LA1RA_2LA1RZ3RA3RB Halt 7195 90 | |||
1RB3LA1LA1RA_2LA1RZ3LA3RB Halt 6445 84 | |||
1RB3LA1LA1RA_2LA1RZ2RA3RB Halt 6445 84 | |||
1RB2RB3LA2RA_1LA3RB1RZ1LB Halt 2351 60 | |||
1RB3RA1LA2RB_2LA3LA1RZ1RA Halt 1021 53 | |||
1RB3LA1RZ0RB_2LB2LA0LA0RA Halt 1001 26 | |||
1RB2LA1RZ3LA_2LA2RB3RB2LB Halt 770 30 | |||
1RB2LB1RZ3LA_2LA2RB3RB2LB Halt 708 29 | |||
1RB2LA0RB1LB_1LA3RA1RA1RZ Halt 592 24 | |||
1RB3LA3RA0LA_2LB1LA1RZ2RA Halt 392 20 | |||
1RB3LA1LA1RA_2LA1RZ2RB3RB Halt 376 21 | |||
1RB3LA1LA1RA_2LA1RZ0LA3RB Halt 376 21 | |||
1RB3LA3RB0LA_2LA1RZ1LB3RA Halt 374 22 | |||
1RB1RA1LB0RA_2LA3RB2RA1RZ Halt 335 18 | |||
1RB2LA3LA1LB_2LA1RZ2RB0RA Halt 292 18 | |||
1RB0RB1RZ0LA_2LA3RA3LA1LB Halt 289 13 | |||
1RB1LA1RZ0LB_2LA3RB1RB2RA Halt 283 18 | |||
1RB3LA3RA0LA_2LB1LA1RZ3RA Halt 266 19 | |||
1RB2RB1RZ1LB_2LA2LB3RB0RB Halt 241 15 | |||
For the top 100 halting BB(2,4) TMs, see: https://github.com/sligocki/busy-beaver/blob/main/Machines/bb/2x4.txt | |||
Revision as of 18:31, 19 August 2024
BB(2,4) was unofficially found to be 3,932,964 on April 10, 2023 by the bbchallenge project, when deciders made for solving BB(5) eliminated the last BB(2,4) holdouts. The champion machine M, with S(M) = 3,932,964 and Σ(M) = 2,050, was found by Terry and Shawn Ligocki in February 2005.
Work formalizing this result is ongoing.
History
- Brady found a steps and ones champion in 1988, establishing S(2,4) ≥ 7195 and Σ(2,4) ≥ 90.[1]
- Terry and Shawn Ligocki found the current champion in 2005.
Champion
S(2,4) = 3,932,964 and Σ(2,4) = 2050 and both are achieved by only one champion (in TNF):
1RB2LA1RA1RA_1LB1LA3RB1RZ(bbch)
Enumeration
The top 20 longest running BB(2,4) TMs (in TNF-1RB) are:
Standard Format Steps Σ 1RB2LA1RA1RA_1LB1LA3RB1RZ Halt 3932964 2050 1RB3LA1LA1RA_2LA1RZ3RA3RB Halt 7195 90 1RB3LA1LA1RA_2LA1RZ3LA3RB Halt 6445 84 1RB3LA1LA1RA_2LA1RZ2RA3RB Halt 6445 84 1RB2RB3LA2RA_1LA3RB1RZ1LB Halt 2351 60 1RB3RA1LA2RB_2LA3LA1RZ1RA Halt 1021 53 1RB3LA1RZ0RB_2LB2LA0LA0RA Halt 1001 26 1RB2LA1RZ3LA_2LA2RB3RB2LB Halt 770 30 1RB2LB1RZ3LA_2LA2RB3RB2LB Halt 708 29 1RB2LA0RB1LB_1LA3RA1RA1RZ Halt 592 24 1RB3LA3RA0LA_2LB1LA1RZ2RA Halt 392 20 1RB3LA1LA1RA_2LA1RZ2RB3RB Halt 376 21 1RB3LA1LA1RA_2LA1RZ0LA3RB Halt 376 21 1RB3LA3RB0LA_2LA1RZ1LB3RA Halt 374 22 1RB1RA1LB0RA_2LA3RB2RA1RZ Halt 335 18 1RB2LA3LA1LB_2LA1RZ2RB0RA Halt 292 18 1RB0RB1RZ0LA_2LA3RA3LA1LB Halt 289 13 1RB1LA1RZ0LB_2LA3RB1RB2RA Halt 283 18 1RB3LA3RA0LA_2LB1LA1RZ3RA Halt 266 19 1RB2RB1RZ1LB_2LA2LB3RB0RB Halt 241 15
For the top 100 halting BB(2,4) TMs, see: https://github.com/sligocki/busy-beaver/blob/main/Machines/bb/2x4.txt
- ↑ Brady A.H. (1988) The busy beaver game and the meaning of life in: The Universal Turing Machine: A Half-Century Survey, R. Herken (Ed.), Oxford University Press, 1988, 259-277.