BB(4)

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Revision as of 08:04, 10 July 2024 by Hsjoihs (talk | contribs) (Created page with "'''BB(4)''' refers to the 4<sup>th</sup> value of the Busy Beaver function. == History == In this Section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations; see Busy Beaver Functions. * In 1966, Allen Brady conjectures Σ(4) = 13 and S(4) = 106.<ref name=":1">Brady, A. H. (1966). The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4. https://ieeexplore.ieee.org/document/4038890 </ref> * In...")
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BB(4) refers to the 4th value of the Busy Beaver function.

History

In this Section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations; see Busy Beaver Functions.

  • In 1966, Allen Brady conjectures Σ(4) = 13 and S(4) = 106.[1]
  • In 1974, Allen Brady proves that S(4) = 107.[2] (better source needed)
  • In 1983, Allen Brady publishes the proof that Σ(4) = 13 and S(4) = 107. [3]


References

  1. ↑ Brady, A. H. (1966). The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4. https://ieeexplore.ieee.org/document/4038890
  2. ↑ https://www.quantamagazine.org/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702/
  3. ↑ Brady, A. H. (1983). The determination of the value of Rado’s noncomputable function Σ(k) for four-state Turing machines. https://www.ams.org/journals/mcom/1983-40-162/S0025-5718-1983-0689479-6/
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