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$\mathrm{\Sigma }$(2,2,2) > 6 but not from this TM

Top

	0	1
A	1RB	0LB
B	0LDA	0RDB

Bottom

	0	1
A	0LUA	1LUB
B	1RA	halt

The Champion for BB(2,2,3) is this. S(2,2,3) > 24 and $\mathrm{\Sigma }$(2,2,3) > 8

Top

	0	1
A	1RDB	halt
B	0LA	halt

Middle

	0	1
A	0RUB	halt
B	0RDA	halt

Bottom

	0	1
A	1LUA	halt
B	1LUB	1LB