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)
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| BLB(3)
|
≥ 34[2]
|
1RB1LB_1LA1LC_1RC0LC (bbch)
|
| BLB(4)
|
≥ 32,779,477
|
1RB1LD_1RC1RB_1LC1LA_0RC0RD (bbch)
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| BLB(5)
|
≥ 455,790,469,746[3][4]
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1RB---_0RC1RB_1LC1LD_1RE0RD_0LE0RB (bbch)
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| BLB(6)
|
|
|
| BLB(7)
|
> 10^183.76332[5]
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1RB0RF_1RC1RA_1LD0LA_0RG0RE_0RA1LF_0LE0LC_1RZ0RD (bbch)
|
| 5 Symbols:
|
Steps
|
Champions
|
| BLB(2,5)
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≥ 166,524,066,023,572,459[6]
|
1RB2RB3LA2RA3RA_2LB1LA0RB4RA4LA (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.
References