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== | ||
| Line 7: | Line 7: | ||
!Steps | !Steps | ||
!Champions | !Champions | ||
|- | |- | ||
|BLB(2) | |BLB(2) | ||
| Line 23: | Line 19: | ||
|<math>\geq 32\,779\,477</math> | |<math>\geq 32\,779\,477</math> | ||
|{{TM|1RB1LD_1RC1RB_1LC1LA_0RC0RD}} | |{{TM|1RB1LD_1RC1RB_1LC1LA_0RC0RD}} | ||
|- | |||
|BLB(5) | |||
|<math>\geq 32\,810\,047</math><ref>Comment #71 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref> | |||
|{{TM|1RB1LC_1RD0LE_0RD0RC_1LD1LA_1RB1RE}} | |||
|- | |||
|BLB(6) | |||
|<math>\geq 65\,538\,549</math><ref>Comment #62 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref> | |||
|{{TM|1RB1LE_1RD1RB_0RD0RE_1LD1LA_0RF1RF_0LC1LC}} | |||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
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!Steps | !Steps | ||
!Champions | !Champions | ||
|- | |- | ||
|BLB(2,3) | |BLB(2,3) | ||
| Line 43: | Line 43: | ||
!Steps | !Steps | ||
!Champions | !Champions | ||
|- | |- | ||
|BLB(2,4) | |BLB(2,4) | ||
| Line 52: | Line 48: | ||
|{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}} | |{{TM|1RB2RA1RA2RB_2LB3LA0RB0RA}} | ||
|} | |} | ||
==See also== | |||
* [[Instruction-Limited Busy Beaver#Instruction-Limited Busy Beaver Variants|Instruction-Limited Blanking Busy Beaver]] | |||
==References== | ==References== | ||
[[Category:Functions]] | [[Category:Functions]] | ||
Latest revision as of 21:01, 26 September 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) | [1] | 1RB0RA_1LB1LA (bbch)
|
| BLB(3) | [2] | 1RB1LB_1LA1LC_1RC0LC (bbch)
|
| BLB(4) | 1RB1LD_1RC1RB_1LC1LA_0RC0RD (bbch)
| |
| BLB(5) | [3] | 1RB1LC_1RD0LE_0RD0RC_1LD1LA_1RB1RE (bbch)
|
| BLB(6) | [4] | 1RB1LE_1RD1RB_0RD0RE_1LD1LA_0RF1RF_0LC1LC (bbch)
|
| 3 Symbols: | Steps | Champions |
|---|---|---|
| BLB(2,3) | [2] | 1RB2LA0RB_1LA0LB1RA (bbch)
|
| 4 Symbols: | Steps | Champions |
|---|---|---|
| BLB(2,4) | [2] | 1RB2RA1RA2RB_2LB3LA0RB0RA (bbch)
|
See also
References
- ↑ Nick Drozd. "Blanking Beavers". Accessed 15 August 2025.
- ↑ 2.0 2.1 2.2 Nick Drozd. "Latest Beeping Busy Beaver Results". Accessed 15 August 2025.
- ↑ Comment #71 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.
- ↑ Comment #62 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.