Thanks for compiling all that.
Here’s a refreshed picture of which known deciders (or verifiers, in case of large numbers in the “FAR” columns) can get the various Skelet machines.
In this version, I’ll leave out the above shawn_oct3 category (which referred to results sligocki shared here). @sligocki and @univerz both have strong rule-proving programs which get some of the Skelet machines.
CPS refers to closed-position-set. At this point, the state of the art is what’s implemented in savask’s and univerz’s versions. The triplet of numbers specifies left/central/right segment sizes which work; the former program details in its comments what this means.
In the FAR column, I give the number of DFA states needed and show which way the DFA reads the tape. (In some cases I only have bounds on the solution size. If you see that, FAR is not the best method to use anyway!)
The FAR-MitM column gives the common left- and right-DFA size for a “meet-in-the-middle DFA” solution.
This is explained in my decider readme; the bbchallenge-proofs repo also has a draft write-up (but it’s commented out). Again, sometimes I only have bounds.
| # | Seed | TranslatedCyclers | Bouncers | CPS | FAR | FAR-MitM |
|---|---|---|---|---|---|---|
| 1 | 68329601 | |||||
| 2 | 55767995 |  |
≤12 | 12 | ||
| 3 | 5950405 | 17 ← | 18 | |||
| 4 | 6897876 | no? | 5 → | 10 | ||
| 5 | 60581745 | |
≤12 | 12 | ||
| 6 | 58211439 | |
≤12 | 12 | ||
| 7 | 7196989 | 17 → | 18 | |||
| 8 | 7728246 | |
10 → | 11 | ||
| 9 | 12554268 | no? | 13 → | <∞ | ||
| 10 | 3810716 | |||||
| 11 | 3810169 | |
10 → | 10 | ||
| 12 | 4982511 | 7 → | 13 | |||
| 13 | 7566785 | 7 ← | 13 | |||
| 14 | 31357173 | |
<∞ | <∞ | ||
| 15 | 2204428 | |||||
| 16 | 20569060 | 11 → | 12 | |||
| 17 | 1365166 | |||||
| 18 | 15439451 | |
1-18-20 | <∞ | <∞ | |
| 19 | 14536286 | 9 → | 11 | |||
| 20 | 347505 | |
8-24-7 | <∞ | <∞ | |
| 21 | 9980689 | |
12-16-14 | <∞ | <∞ | |
| 22 | 45615747 | |
<∞ | <∞ | ||
| 23 | 6237150 | 18-24-17 | 6 → | 9 | ||
| 24 | 60658955 | 11 → | 11 | |||
| 25 | 47260245 | |
16-5-4 | 2 | 5 | |
| 26 | 13134219 | |||||
| 27 | 7163434 | 7-7-7 | 7 → | 9 | ||
| 28 | 5657318 | |
16-16-17 | <∞ | <∞ | |
| 29 | 6626162 | 18-24-17 | 6 → | 9 | ||
| 30 | 4986661 | 20-20-19 | 41 ← | <∞ | ||
| 31 | 56967673 | |
1-17-9 | 195 ← | <∞ | |
| 32 | 6957734 | no? | 1 → | 3 | ||
| 33 | 11896833 | |||||
| 34 | 11896832 | |||||
| 35 | 11896831 | |||||
| 36 | 13609549 | 5 → | 7 | |||
| 37 | 7512832 | 5 ← | 8 | |||
| 38 | 35771936 | 11 → | 11 | |||
| 39 | 9914965 | |
16-12-24 | <∞ | <∞ | |
| 40 | 3841616 | 4 → | 4 | |||
| 41 | 5915217 | 20-20-20 | 40 → | <∞ | ||
| 42 | 57874080 | 9 → | 11 | |||
| 43 | 5878998 | 14-14-14 | 50 → | <∞ |