BitChanger Busy beaver

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Counting instructions

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.

Confirmed optimal

These are confirmed to be the best for lengths 1-14. Time' and Program' count ] as two steps instead (jump to [, followed by [ itself.)

length Time Program Time' Program'
0 0 0
1 1 } 1 }
2 2 }} 2 }}
3 3 }}} 3 }}}
4 4 }}}} 4 }}}}
5 5 }}}}} 6 }<[}]
6 8 }}<[<] 10 }}<[<]
7 11 }}}<[<] 14 }}}<[<]
8 14 }}}}<[<] 18 }}}}<[<]
9 17 }}}}}<[<] 22 }}}}}<[<]
10 22 }}}}<[}<<] 26 }}}}}}<[<]
11 27 }}}}}<[}<<] 35 }}}<[[<]}}]
12 36 }}}}<[[<]}}] 47 }}}}<[[<]}}]
13 45 }}}}}<[[<]}}] 59 }}}}}<[[<]}}]
14 58 }<[}}<<<[<]}}] 71 }}}}}}<[[<]}}]

See BitChanger Busy beaver/Proof for details.

Longer lengths

 }}}}<[}[}<}]}<[}[}<}]}<[}[}<}]}<[<]}<<]}<<] 43 characters

originally from

 >+>+>+>+[+>[>]+[+>[>]+[+>[>]+[<]+<]+<]+<]

See also