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
| 3 Symbols:
|
Steps
|
Champions
|
| BLB(2,3)
|
77[2]
|
1RB2LA0RB_1LA0LB1RA (bbch)
|
| BLB(3,3)
|
> 1042,745
|
1RB2RB1LA_2LC0LB2LB_2RC2RA0LC (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)
|
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