$Id: bb-list,v 1.3 2000/08/17 00:22:34 heiner Exp $
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5-state Turing machines found by Heiner Marxen and Juergen Buntrock.
The following table lists for each input state and symbol the output state,
symbol and tape movement. The initial state is A, the halting state is H.
No A0 A1 B0 B1 C0 C1 D0 D1 E0 E1 ones steps
1 B1L C1R C1L B1L D1L E0R A1R D1R H1L A0R 4098 47176870
2 B1L A1L C1R B1R A1L D1R A1L E1R H1R C0R 4098 11798826
3 B1L D0R C1R D1L A1R C1R H1L E1L A1L B0L 4097 23554764
4 B1L A1L C1R D1L A1R C1R H1L E0L C1R B1L 4097 11798796
5 B1L A1L C1R D0L A1R C1R H1L E1L E0R B1L 4096 11804910
6 B1L A1L C1R D0L A1R C1R H1L E1L C1R B1L 4096 11804896
7 B1L D1L C1R E0R A0L B0R E1L H1L C1R C1L 1471 2358064 (similar to Uhing's)
The number of steps for No 3 erroneously had been stated to be four larger.
Above is given the corrected value. It has been corrected first by
Pascal Michel, "Busy beaver competition and Collatz-like problems",
Arch. Math. Logic, 32 (1993) pp 351-367
and has been noted here at 01-Feb-1998.
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6-state Turing machines found by Heiner Marxen and Juergen Buntrock.
No A0 A1 B0 B1 C0 C1 D0 D1 E0 E1 F0 F1 ones steps
1 B1L A1L C1R B1R F0R D1R A1L E0R A0L C1R E1L H1L 136612 13122572797
2 B1R A1R C1L B1L F0R D1L A1R E0L H1L F1L A0L C0L 95524079 8690333381690951
3 B1R C0R A0L D0R D1R H1R E1L D0L F1R B1L A1R E1R
ones = 2,537,699,363,594,175,843,063
steps = 5,366,598,383,321,904,238,506,234,609,927,865,294,538,105
No 1 has been verified independently (private communication) by
- Robert Harley (11 Sep 1997)
- Dr. Bryant Julstrom of St.Cloud State University (6 Oct 1997)
- Michael Grey (of SCSU) (6 Oct 1997)
No 2 has been verified independently by Anatoly Vorobey
at 20 Sep 1997. He was the first to detect that the original number of steps
were one too large (corrected above).
No 3 was found in July 2000. Chris Thompson independently
verified the number of ones (11 Aug 2000), and the final configuration:
1^2537699363594175843062 0 1 0(H)
He also provided the above number of steps (14 Aug 2000), which is not yet
verified independently.