Multidimensional Turing Machine
This is a work in progress.
A multidimensional Turing Machine is a Turing Machine that use a multidimensional tape instead. These Turing Machines have (2*dimension count) different moving directions, 2 each for 1 dimension.
Example: 1RB0UA_1DA0LB is a 2-dimensional Turing Machine, used L, R, U (Up), D (Down) 4 moving directions, and 1RB0FA_1DA0LC_1BC0UA is a 3-dimensional Turing Machine, used L, R, U, D, F (Front), B (Back) 6 moving directions.
BB_2D(n,m) = Maximum number of steps taken by a halting n-state, m-symbol 2D Turing machine starting from a blank (all 0) 2D tape, BB_3D(n,m) = Maximum number of steps taken by a halting n-state, m-symbol 3D Turing machine starting from a blank (all 0) 3D tape and BB_MD(n,m) = Maximum number of steps taken by a halting n-state, m-symbol multidimensional Turing machine starting from a blank (all 0) multidimensional tape (which uses at most n*m-1 dimensions).
Values
Note: Champions are not TNF form.
| Domain | Runtime | Champion |
|---|---|---|
| BB_2D(2) | >= 6 | Same as BB(2) |
| BB_2D(3) | >= 32 | 1DB1LC_0LC0RB_1UA1RZ
|
| BB_2D(4) | >= 4,632 | 1RB0DB_1UD1RC_0LA1UC_1LA1RZ
|
| BB_2D(5) | >= 25,772,988,638 | 1UB1RZ_1DC0LD_0RE0RD_1LA0LB_0UA0UB
|
| BB_2D(2,3) | >= 38 | Same as BB(2,3) |
| Domain | Score | Champion |
|---|---|---|
| BB_2D(2) | >= 4 | Same as BB(2) |
| BB_2D(3) | >= 11 | 1LC1RB_1DA1UB_1UB1RZ
|
| BB_2D(4) | >= 244 | 1RB0LA_1LD1DA_1DA1RZ_1LC1UD
|
| BB_2D(5) | >= 935,508,401 | 1UB1RZ_0RC1UD_1DE0LD_1UC1DD_1LD0RA
|
| BB_2D(2,3) | >= 10 | 1UB2LB0RA_1DA2UB1RZ
|
Tree Normal Form
TNF for multidimensional Turing Machine is same as TNF for 1D Turing Machine, except you can use multidimensional choice for transition. The choice will have additional restrictions:
- The next direction of a transition may be any previously visited dimension or the next unvisited dimension.
- If we are expanding the first transition of a new dimension, the direction must be positive for this dimension. (e.g. R, U, F).
External Links
https://github.com/GollyGang/ruletablerepository/wiki/TwoDimensionalTuringMachines