Multi-tape Turing Machines
Multi-tape Turing Machines are like normal Turing machines but with more tapes. BB(n,m,o) = the maximum number of steps taken by a n state, m symbol, o tape Turing machine. In addition to going left and right, it can also go up and down. All of the champions have been hand simulated (which hopefully will change soon) which means that none of them will be optimal at all.
Rules
- Going up or down is not required for each step.
- The head starts on the lowermost tape.
- A step can just be going up or down.
- Each tape needs it own instructions
- BB(n,m,1) = BB(n,m)
How to write TMswriting 2d TMs are mostly like writing them in the first dimension. You just need to add a slash in between every layer of instruction.
The champion for BB(2,2,2) would be this in TM form - 1RB0LB_0LDA0RDB / 0LUA1LUB_1RA1RZ
The Champion for BB(2,2,2) is this. S(2,2,2) > 16. Sigma(2,2,2) > 6 but not from this TM
| 0 | 1 | |
| A | 1RB | 0LB |
| B | 0LDA | 0RDB |
| 0 | 1 | |
| A | 0LUA | 1LUB |
| B | 1RA | halt |
The Champion for BB(2,2,3) is this. S(2,2,3) > 24 and (2,2,3) > 8
| 0 | 1 | |
| A | 1RDB | halt |
| B | 0LA | halt |
| 0 | 1 | |
| A | 0RUB | halt |
| B | 0RDA | halt |
| 0 | 1 | |
| A | 1LUA | halt |
| B | 1LUB | 1LB |