BitChanger Busy beaver
Counting instructions (convention 1)
Both } and < count as 1 instruction.
Both entering and skipping a [ count as 1 instruction.
Every time reach a ] we either skip past it counting 1 instruction or we jump directly after the matching [ also counting 1 instruction.
Counting instructions (convention 2)
Both } and < count as 1 instruction.
Both entering and skipping a [ count as 1 instruction.
Every time reach a ] we jump directly to directly to the matching [ counting 1 instruction.
Confirmed optimal
These are confirmed to be the best for lengths 0-21. S' and PS' count ] as two steps instead (jump to [, followed by [ itself.)
Σ is the maximum amount of bits the program can leave at the tape before halting.
Ψ is the maximum space at any point a halting problem can reach.
| n | S(n) | PS | S'(n) | PS' | Σ(n) | PΣ | Ψ(n) | PΨ |
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | |
0 | |
0 | |
0 | |
| 1 | 1 | } |
1 | } |
1 | } |
1 | <
|
| 2 | 2 | }} |
2 | }} |
2 | }} |
2 | <<
|
| 3 | 3 | }}} |
3 | }}} |
3 | }}} |
3 | <<<
|
| 4 | 4 | }}}} |
4 | }}}} |
4 | }}}} |
4 | <<<<
|
| 5 | 5 | }}}}} |
6 | }<[}] |
5 | }}}}} |
5 | <<<<<
|
| 6 | 8 | }}<[<] |
10 | }}<[<] |
6 | }}}}}} |
6 | <<<<<<
|
| 7 | 11 | }}}<[<] |
14 | }}}<[<] |
7 | }}}}}}} |
7 | <<<<<<<
|
| 8 | 14 | }}}}<[<] |
18 | }}}}<[<] |
8 | }}}}}}}} |
8 | <<<<<<<<
|
| 9 | 17 | }}}}}<[<] |
22 | }}}}}<[<] |
9 | }}}}}}}}} |
9 | <<<<<<<<<
|
| 10 | 22 | }}}}<[}<<] |
26 | }}}}}}<[<] |
10 | }}}}}}}}}} |
10 | <<<<<<<<<<
|
| 11 | 27 | }}}}}<[}<<] |
35 | }}}<[[<]}}] |
11 | }}}}}}}}}}} |
11 | <<<<<<<<<<<
|
| 12 | 36 | }}}}<[[<]}}] |
47 | }}}}<[[<]}}] |
12 | }}}}}}}}}}}} |
12 | <<<<<<<<<<<<
|
| 13 | 45 | }}}}}<[[<]}}] |
59 | }}}}}<[[<]}}] |
13 | }}}}}}}}}}}}} |
13 | <<<<<<<<<<<<<
|
| 14 | 58 | }<[}}<<<[<]}}] |
71 | }}}}}}<[[<]}}] |
14 | }}}}}}}}}}}}}} |
14 | <<<<<<<<<<<<<<
|
| 15 | 252 | }<[}}<[<<<}]}}] |
295 | }<[}}<[<<<}]}}] |
15 | }}}}}}}}}}}}}}} |
17 | }<[}}<[<<<}]}}]
|
| 16 | 253 | <}<[}}<[<<<}]}}] |
296 | <}<[}}<[<<<}]}}] |
16 | }}}}}}}}}}}}}}}} |
17 | }<[}}<[<<<}]}}]}
|
| 17 | ? | ? |
346 | }<[[}}<[<<<}]]}}] |
17 | }}}}}}}}}}}}}}}}} |
17 | <<<<<<<<<<<<<<<<<
|
| 18 | ? | ? |
367 | }<[[}}<[<<<}]}}]}] |
18 | }}}}}}}}}}}}}}}}}} |
28 | }}<[<[<<<]}[}}}]<]
|
| 19 | ? | ? |
759 | }<[}}<}}}<[[<]<]}}] |
23 | }<[}}<}}}<[[<]<]}}] |
36 | }<[}}<}}}<[[<]<]}}]
|
| 20 | ? | ? |
11445 | }<[[<<}<[}<}]}]<<<}] |
40 | }<[[<<}<[}<}]}]<<<}] |
61 | }<[[<<}<[}<}]}]<<<}]
|
| 21 | ? | ? |
11446 | <}<[[<<}<[}<}]}]<<<}] |
77 | }<[[}<}}}}<[<}<<]}]}] |
88 | }<[[}<}}}}<[<}<<]}]}]
|
See BitChanger Busy beaver/Proof for details.
Longer lengths
}}}}<[}[}<}]}<[}[}<}]}<[}[}<}]}<[<]}<<]}<<] 43 characters
originally from
>+>+>+>+[+>[>]+[+>[>]+[+>[>]+[<]+<]+<]+<]