Blanking Busy Beaver Function: Difference between revisions

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The '''Blanking Busy Beaver Function''' (BLB(n,m)) is a [[Busy Beaver Functions|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.
The '''Blanking Busy Beaver Function''' (BLB(n,m)) is a [[Busy Beaver Functions|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 [[BB(n,1)|1-symbol machines]] is always blank.


==Champions==
== Champions ==
{| class="wikitable"
|+
!'''2 Symbols:'''
!Steps
!Champions
|-
|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}}
|-
|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}}
|-
|BLB(4)
|≥ 32,779,477
|{{TM|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
|-
|BLB(5)
|≥ 32,810,047<ref>Comment #71 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref>
|{{TM|1RB1LC_1RD0LE_0RD0RC_1LD1LA_1RB1RE}}
|-
|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}}
|}
{| class="wikitable"
|+
!'''3 Symbols:'''
!Steps
!Champions
|-
|BLB(2,3)
|≥ 77<ref name=":4" />
|{{TM|1RB2LA0RB_1LA0LB1RA}}
|}
{| class="wikitable"
|+
!'''4 Symbols:'''
!Steps
!Champions
|-
|BLB(2,4)
|≥ 1,367,361,263,049<ref name=":4" />
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}}
|}


== [[Instruction-Limited Busy Beaver|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.
{| class="wikitable"
|+
!Instructions
!Steps
!Champions
|-
|BLBi(3)
|4
|?
|-
|BLBi(4)
|12
|?
|-
|BLBi(5)
|30
|?
|-
|BLBi(6)
|77
|{{TM|1RB2LA0RB_1LA0LB1RA}}
|-
|BLBi(7)
|808
|?
|-
|BLBi(8)
|≥ 1,367,361,263,049
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}}
|}
==References==
[[Category:Functions]]
[[Category:Functions]]

Latest revision as of 12:58, 26 December 2025

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: Steps 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) ≥ 32,810,047[3] 1RB1LC_1RD0LE_0RD0RC_1LD1LA_1RB1RE (bbch)
BLB(6) ≥ 65,538,549[4] 1RB1LE_1RD1RB_0RD0RE_1LD1LA_0RF1RF_0LC1LC (bbch)
3 Symbols: Steps Champions
BLB(2,3) ≥ 77[2] 1RB2LA0RB_1LA0LB1RA (bbch)
4 Symbols: Steps Champions
BLB(2,4) ≥ 1,367,361,263,049[2] 1RB2RA1RA2RB_2LB3LA0RB0RA (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 ?
BLBi(4) 12 ?
BLBi(5) 30 ?
BLBi(6) 77 1RB2LA0RB_1LA0LB1RA (bbch)
BLBi(7) 808 ?
BLBi(8) ≥ 1,367,361,263,049 1RB2RA1RA2RB_2LB3LA0RB0RA (bbch)

References

  1. ↑ Nick Drozd. "Blanking Beavers". Accessed 15 August 2025.
  2. ↑ 2.0 2.1 2.2 Nick Drozd. "Latest Beeping Busy Beaver Results". Accessed 15 August 2025.
  3. ↑ Comment #71 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.
  4. ↑ Comment #62 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.
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