Machine config of the 23,554,764-halter found by bbchallenge

Individual machines
1

Hi, I would be interested to know the machine config, and if it exists, any analysis of the halter found by the bbchallenge project which takes 23,554,764 steps.

The number of steps is reasonably close to half the step count of Marxen and Buntrock’s record-holder and I would like to know whether this machine is a variant on theirs using the same Collatz transformation, or if this is simply a coincidence.

2

Shawn’s program gives the below final config, step count, and nonzero tape symbol count. Unsure if there are deeper analyses out there.

[justinb@husk busy-beaver]$ pypy3 Code/Quick_Sim.py <(echo 1RB0LD_1LC1RD_1LA1LC_1RZ1RE_1RA0RB)

Transition table:

       +-----+-----+
       |  0  |  1  |
   +---+-----+-----+
   | A | 1RB | 0LD |
   +---+-----+-----+
   | B | 1LC | 1RD |
   +---+-----+-----+
   | C | 1LA | 1LC |
   +---+-----+-----+
   | D | 1RZ | 1RE |
   +---+-----+-----+
   | E | 1RA | 0RB |
   +---+-----+-----+


BF: Searching for optimal block size
BF: Least compressed tape at step 5698 : 111011011011011011011011011011011011011011011011011011011011011011011011011011011011011011011011011
BF: Optimal tape compression block size 3 tape size 9
BF: Searching for optimal mult for block size 3
BF: * 1 188.09809488718872
BF: * 2 96.004911733264
BF: * 3 66.14871295496721
BF: Block Finder finished

best_block_size: 3
elapsed_time_us: 3181870
least_compressed_loop: 4333
least_compressed_tape_size_chain: 68
least_compressed_tape_size_raw: 99
best_compression_block_size: 3
best_compression_tape_size: 9
best_mult: 1
best_chain_factor: 188.0981


         Steps:                     Times Applied:
Total:                                           0
Macro:                                           0
Chain:                                           0
Rule:                                            0
Rules proven: 0
Failed proofs: 0
Prover num past configs: 0
Tape copies: 0
Elapsed time: 0.0014963150024414062
000^inf (000) A> 000^inf
Num Nonzeros:   0

         Steps:                     Times Applied:
Total:   10^7.4                                415
Macro:   10^3.3                                254
Chain:   10^5.2                                152
Rule:    10^7.4                                  9
Rules proven: 3
Failed proofs: 6
Prover num past configs: 14
Tape copies: 47
Elapsed time: 0.6076445579528809
000^inf 001^1 110^2047 (110) Z> 000^inf
Num Nonzeros: 10^3.6  4097

Turing Machine Halted

Steps:    23554764
Nonzeros: 4097
3

Thank you so much for this.

Looks like it is also based on a Collatz transform 3k + a → 5k + c with 1 in 3 of the residues modulo 3 leading to halting. However, superficially it looks like it’s not the same transformation.

However, it seems to zig-zag at half the speed, and so it adds width quadratically at 1/sqrt(2) of the speed of the champion, and it finishes with used tape almost exactly half as long but with twice the density of 1s, for almost exactly the same number of 1s. So the numerical coincidence is still hard to dismiss without being able to say how weird collatz problems relate to other similar weird collatz problems.