Blanking Beaver: Difference between revisions

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MAde citations consistent with Measuring large numbers page
 
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!'''2 Symbols:'''
!'''2 Symbols:'''
!Steps
!Halting Steps
!Champions
!Non-Halting Steps
!Halting Champions
!Non-Halting Champions
|-
|-
|BLB(2)
|BLB(2)
|≥ 8<ref name=":3">Nick Drozd. "[https://nickdrozd.github.io/2021/02/14/blanking-beavers.html Blanking Beavers]". Accessed 15 August 2025.</ref>
|
|{{TM|1RB0RA_1LB1LA}}
|8<ref name=":3">Nick Drozd, "[https://nickdrozd.github.io/2021/02/14/blanking-beavers.html Blanking Beavers]". Blog post, February 2021. Accessed 15 August 2025.</ref>
|
|{{TM|1RB0RA_1LB1LA|non_halt}}
|-
|-
|BLB(3)
|BLB(3)
|≥ 34<ref name=":4">Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref>
|
|{{TM|1RB1LB_1LA1LC_1RC0LC}}
|34<ref name=":4">Nick Drozd, "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Blog post, February 2022. Accessed 15 August 2025.</ref>
|
|{{TM|1RB1LB_1LA1LC_1RC0LC|non_halt}}
|-
|-
|BLB(4)
|BLB(4)
|
|≥ 32,779,477
|≥ 32,779,477
|{{TM|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
|
|{{TM|1RB1LD_1RC1RB_1LC1LA_0RC0RD|non_halt}}
|-
|-
|BLB(5)
|BLB(5)
|≥ 32,810,047<ref>Comment #71 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref>
|
|{{TM|1RB1LC_1RD0LE_0RD0RC_1LD1LA_1RB1RE}}
|> 10<sup>14,006</sup>
|
|{{TM|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA|non_halt}}
|-
|-
|BLB(6)
|BLB(6)
|≥ 65,538,549<ref>Comment #62 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref>
|
|{{TM|1RB1LE_1RD1RB_0RD0RE_1LD1LA_0RF1RF_0LC1LC}}
|> 10 ↑↑ 16
|
|{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RE_1LF0RB_0RC0RE|non_halt}}
|-
|BLB(7)
|> 10^183.76332<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1374531970830307409</ref>
|
|{{TM|1RB0RF_1RC1RA_1LD0LA_0RG0RE_0RA1LF_0LE0LC_1RZ0RD|halt}}
|
|}
|}
{| class="wikitable"
{| class="wikitable"
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|-
|-
|BLB(2,3)
|BLB(2,3)
|≥ 77<ref name=":4" />
|77<ref name=":4" />
|{{TM|1RB2LA0RB_1LA0LB1RA}}
|{{TM|1RB2LA0RB_1LA0LB1RA}}
|-
|BLB(3,3)
|> 10 ↑↑ 6.54<ref name=":Nick Drozd Tetrational Blank26">Nick Drozd, "[https://nickdrozd.github.io/2026/09/01/tetrational-self-cleaning-turing-machine.html A Tetrational Self-Cleaning Turing Machine]". Blog post, September 2026. Accessed 17 October 2026.</ref>
|{{TM|1RB1RC2RA_0RC2RA0RB_2LC2LB0LA}}
|}
|}
{| class="wikitable"
{| class="wikitable"
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|≥ 1,367,361,263,049<ref name=":4" />
|≥ 1,367,361,263,049<ref name=":4" />
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}}
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}}
|}
{| class="wikitable"
|+
!'''5 Symbols:'''
!Steps
!Champions
|-
|BLB(2,5)
|> 10<sup>32</sup>
|{{TM|1RB2RB4RA0RB2RA_2LB3LA0RB0RA1RB}}
|}
|}


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|BLBi(3)
|BLBi(3)
|4
|4
|?
|{{TM|1RB0RA_1LA---}}
|-
|-
|BLBi(4)
|BLBi(4)
|12
|12
|?
|{{TM|1RB---_1RC---_1LC0RC}}
|-
|-
|BLBi(5)
|BLBi(5)
|30
|30
|?
|{{TM|1RB------_1RC------_2LC2RC0RC}}
|-
|-
|BLBi(6)
|BLBi(6)
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|BLBi(7)
|BLBi(7)
|808
|808
|?
|{{TM|1RB------_1RC------_0RD2LC---_1LD2RD0RC}}
|-
|-
|BLBi(8)
|BLBi(8)
|≥ 1,367,361,263,049
|≥ 1,367,361,263,049
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}}
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}}
|-
|BLBi(9)
|> 10<sup>42,745</sup>
|{{TM|1RB2RB1LA_2LC0LB2LB_2RC2RA0LC}}
|}
|}


==References==
==References==
[[Category:Functions]]
[[Category:Functions]]

Latest revision as of 12:18, 17 October 2026

The Blanking Busy Beaver Function (BLB(n,m)) is a Busy Beaver Function which measures the largest amount of steps done by any Turing machine with n states and m symbols before blanking the tape. Blanking Busy Beaver machines are allowed to be halting or non-halting. As machines with just a single state cannot blank the tape, BLB(1,m) is nonexistent for any amount of symbols m. Similarly, BLB(n,1) is nonexistent for any amount of states n, as the tape of 1-symbol machines is always blank.

Champions

2 Symbols: Halting Steps Non-Halting Steps Halting Champions Non-Halting Champions
BLB(2) 8[1] 1RB0RA_1LB1LA (bbch)
BLB(3) 34[2] 1RB1LB_1LA1LC_1RC0LC (bbch)
BLB(4) ≥ 32,779,477 1RB1LD_1RC1RB_1LC1LA_0RC0RD (bbch)
BLB(5) > 1014,006 1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA (bbch)
BLB(6) > 10 ↑↑ 16 1RB0LD_1RC0RF_1LC1LA_0LE1RE_1LF0RB_0RC0RE (bbch)
BLB(7) > 10^183.76332[3] 1RB0RF_1RC1RA_1LD0LA_0RG0RE_0RA1LF_0LE0LC_1RZ0RD (bbch)
3 Symbols: Steps Champions
BLB(2,3) 77[2] 1RB2LA0RB_1LA0LB1RA (bbch)
BLB(3,3) > 10 ↑↑ 6.54[4] 1RB1RC2RA_0RC2RA0RB_2LC2LB0LA (bbch)
4 Symbols: Steps Champions
BLB(2,4) ≥ 1,367,361,263,049[2] 1RB2RA1RA2RB_2LB3LA0RB0RA (bbch)
5 Symbols: Steps Champions
BLB(2,5) > 1032 1RB2RB4RA0RB2RA_2LB3LA0RB0RA1RB (bbch)

Instruction-limited Blanking Busy Beaver (BLBi(n))

BLBi(n) is the largest amount of steps taken by an n-instruction Turing machine when blanking the tape for the first time after having written a non-blank symbol on the tape.

Champions

Note that BLBi(1) and BLBi(2) are nonexistent as Turing machines with one or two instructions cannot blank the tape.

Instructions Steps Champions
BLBi(3) 4 1RB0RA_1LA--- (bbch)
BLBi(4) 12 1RB---_1RC---_1LC0RC (bbch)
BLBi(5) 30 1RB------_1RC------_2LC2RC0RC (bbch)
BLBi(6) 77 1RB2LA0RB_1LA0LB1RA (bbch)
BLBi(7) 808 1RB------_1RC------_0RD2LC---_1LD2RD0RC (bbch)
BLBi(8) ≥ 1,367,361,263,049 1RB2RA1RA2RB_2LB3LA0RB0RA (bbch)
BLBi(9) > 1042,745 1RB2RB1LA_2LC0LB2LB_2RC2RA0LC (bbch)

References

  1. ↑ Nick Drozd, "Blanking Beavers". Blog post, February 2021. Accessed 15 August 2025.
  2. ↑ 2.0 2.1 2.2 Nick Drozd, "Latest Beeping Busy Beaver Results". Blog post, February 2022. Accessed 15 August 2025.
  3. ↑ https://discord.com/channels/960643023006490684/1369339127652159509/1374531970830307409
  4. ↑ Nick Drozd, "A Tetrational Self-Cleaning Turing Machine". Blog post, September 2026. Accessed 17 October 2026.
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