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)
|
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