Busy Beaver for SKI calculus - Revision history

Polygon: Linked BBlambda

2026-04-04T16:18:39Z

Linked BBlambda

← Older revision		Revision as of 16:18, 4 April 2026
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	Busy Beaver for SKI calculus (we will call it BBSKI for now) is a variation of the Busy Beaver problem for lambda calculus.		Busy Beaver for SKI calculus (we will call it BBSKI for now) is a variation of the [[Busy Beaver for lambda calculus\|Busy Beaver problem for lambda calculus]].

	A SKI calculus program is a binary tree where the leaves are combinators, the three symbols <code>S</code>, <code>K</code>, <code>I</code>. Using parentheses to notate the tree, a simple example of a SKI program is <code>(((SK)S)((KI)S))</code>. We can omit parentheses by assuming they are left-binding by default, so we simplify our program to <code>SKS(KIS)</code>.		A SKI calculus program is a binary tree where the leaves are combinators, the three symbols <code>S</code>, <code>K</code>, <code>I</code>. Using parentheses to notate the tree, a simple example of a SKI program is <code>(((SK)S)((KI)S))</code>. We can omit parentheses by assuming they are left-binding by default, so we simplify our program to <code>SKS(KIS)</code>.

Polygon: used proper greater/equals sign

2025-12-25T13:21:17Z

used proper greater/equals sign

← Older revision		Revision as of 13:21, 25 December 2025
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	\|-		\|-
	\|7		\|7
	\|>= 18		\|≥ 18
	\|S(SSS(SI)S)		\|S(SSS(SI)S)
	\|?		\|?
	\|-		\|-
	\|8		\|8
	\|>= 19		\|≥ 19
	\|SS(SSS(SI)S)		\|SS(SSS(SI)S)
	\|?		\|?
	\|-		\|-
	\|9		\|9
	\|>= 519		\|≥ 519
	\|SSI((S(SS)S)S)K		\|SSI((S(SS)S)S)K
	\|?		\|?
	\|-		\|-
	\|10		\|10
	\|>= 1041		\|≥ 1041
	\|SSI((S(SS)S)S)KS		\|SSI((S(SS)S)S)KS
	\|?		\|?
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	\| 5 \|\| = 6 \|\| <code>SSS(SS)</code> \|\| ?		\| 5 \|\| = 6 \|\| <code>SSS(SS)</code> \|\| ?
	\|-		\|-
	\| 6 \|\| >= 8 \|\| <code>SSS(SSS)</code> \|\| ?		\| 6 \|\| ≥ 8 \|\| <code>SSS(SSS)</code> \|\| ?
	\|-		\|-
	\|7		\|7
	\|>= 10		\|≥ 10
	\|<code>SSS(SSSS)</code>		\|<code>SSS(SSSS)</code>
	\|?		\|?
	\|-		\|-
	\|8		\|8
	\|>= 23		\|≥ 23
	\|<code>SSS(S(SKS))S</code>		\|<code>SSS(S(SKS))S</code>
	\|?		\|?

Azerty: Added SK calculus section.

2025-12-24T16:42:54Z

Added SK calculus section.

@@ Line 1: / Line 1: @@
 Busy Beaver for SKI calculus (we will call it BBSKI for now) is a variation of the Busy Beaver problem for lambda calculus.
 == Champions ==
@@ Line 18: / Line 30: @@
 |-
 |7
-|?
+|>= 18
-|?
+|S(SSS(SI)S)
 |?
 |-
 |8
-|?
+|>= 19
-|?
+|SS(SSS(SI)S)
 |?
 |-
@@ Line 35: / Line 47: @@
 |>= 1041
 |SSI((S(SS)S)S)KS
 |?
 |}

Polygon: Added category:functions

2025-11-29T10:21:49Z

Added category:functions

← Older revision		Revision as of 10:21, 29 November 2025
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	== See Also ==		== See Also ==
	[https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this function]		[https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this function]

			[[Category:Functions]]

Azerty: Added a few values to the table.

2025-11-28T13:00:28Z

Added a few values to the table.

@@ Line 16: / Line 16: @@
 |-
 | 6 || = 17 || SSS(SI)S || ?
 |}
 == See Also ==
 [https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this function]

Azerty: Improved the 6th champion.

2025-11-28T12:52:07Z

Improved the 6th champion.

← Older revision		Revision as of 12:52, 28 November 2025
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	\| 5 \|\| = 6 \|\| SSS(SS) \|\| ?		\| 5 \|\| = 6 \|\| SSS(SS) \|\| ?
	\|-		\|-
	\| 6 \|\| >= 8 \|\| SSS(~~SSS~~) \|\| ?		\| 6 \|\| = 17 \|\| SSS(SI)S \|\| ?
	\|}		\|}

	== See Also ==		== See Also ==
	[https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this function]		[https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this function]

Azerty: Created page with "Busy Beaver for SKI calculus (we will call it BBSKI for now) is a variation of the Busy Beaver problem for lambda calculus. == Champions == {| class="wikitable" ! n !! Value !! Champion !! Discoverered by |- | 1 || = 1 || S || ? |- | 2 || = 2 || SS || ? |- | 3 || = 3 || SSS || ? |- | 4 || = 4 || SSSS || ? |- | 5 || = 6 || SSS(SS) || ? |- | 6 || >= 8 || SSS(SSS) || ? |} == See Also == [https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this..."

2025-11-28T12:45:37Z

Created page with "Busy Beaver for SKI calculus (we will call it BBSKI for now) is a variation of the Busy Beaver problem for lambda calculus. == Champions == {| class="wikitable" ! n !! Value !! Champion !! Discoverered by |- | 1 || = 1 || S || ? |- | 2 || = 2 || SS || ? |- | 3 || = 3 || SSS || ? |- | 4 || = 4 || SSSS || ? |- | 5 || = 6 || SSS(SS) || ? |- | 6 || >= 8 || SSS(SSS) || ? |} == See Also == [https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this..."

New page

Busy Beaver for SKI calculus (we will call it BBSKI for now) is a variation of the Busy Beaver problem for lambda calculus.

== Champions ==
{| class="wikitable"
! n !! Value !! Champion !! Discoverered by
|-
| 1 || = 1 || S || ?
|-
| 2 || = 2 || SS || ?
|-
| 3 || = 3 || SSS || ?
|-
| 4 || = 4 || SSSS || ?
|-
| 5 || = 6 || SSS(SS) || ?
|-
| 6 || >= 8 || SSS(SSS) || ?
|}

== See Also ==
[https://komiamiko.me/math/ordinals/2020/06/21/ski-numerals.html Lower bounds of this function]