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=== [[bbchallenge]] === | === [[bbchallenge.org]] === | ||
[[bbchallenge.org]] <ref name=":0" /> is a massively collaborative research project whose general goal is to obtain more knowledge on the [[Busy Beaver function]]. In practice, it mainly consists in collaboratively building [[Deciders]], programs that automatically prove that some [[Turing machines]] do not halt. Some of these [[Deciders]] leverage theorem provers such as [https://en.wikipedia.org/wiki/Coq_(software) Coq]. | |||
==Notes== | ==Notes== | ||
<references /> | <references /> | ||
Revision as of 10:20, 8 June 2024
The Busy Beaver function BB (called S originally) was introduced by Tibor Radó in 1962 [1] for 2-symbol Turing machines and later generalised[2] to m-symbol Turing machines:
| BB(n,m) = Maximum number of steps done by a halting m-symbol Turing machine with n states starting from all-0 memory tape |
The busy beaver function is not computable and, few of its values are known:
| 2-state | 3-state | 4-state | 5-state | 6-state | |
| 2-symbol | BB(2) = 6 | BB(3) = 21 | BB(4) = 107 | BB(5) = 47,176,870 | BB(6) > |
| 3-symbol | BB(2,3) = 38 | BB(3,3) > | BB(4,3) > | ||
| 4-symbol | BB(2,4) = 3,932,964 | BB(3,4) > 2(^15)5 + 14 | |||
| 5-symbol | BB(2,5) > 6.5 × |
In the above table, cells are highlighted in orange when there are known machines in that class that are believed hard to prove halting or non-halting (although, generally believed non-halting), such as Cryptids.
bbchallenge.org
bbchallenge.org [4] is a massively collaborative research project whose general goal is to obtain more knowledge on the Busy Beaver function. In practice, it mainly consists in collaboratively building Deciders, programs that automatically prove that some Turing machines do not halt. Some of these Deciders leverage theorem provers such as Coq.
Notes
- ↑ Rado, T. (1962), On Non-Computable Functions. Bell System Technical Journal, 41: 877-884. https://doi.org/10.1002/j.1538-7305.1962.tb00480.x
- ↑ Brady, Allen H, and the Meaning of Life, 'The Busy Beaver Game and the Meaning of Life', in Rolf Herken (ed.), The Universal Turing Machine: A Half-Century Survey (Oxford, 1990; online edn, Oxford Academic, 31 Oct. 2023), https://doi.org/10.1093/oso/9780198537748.003.0009, accessed 8 June 2024.
- ↑ https://bbchallenge.org/~pascal.michel/ha.html
- ↑ 4.0 4.1 https://bbchallenge.org/