PIsaacson wrote:Aran,

I have to admit that I really don't know what to make of what I've called Type 1 DBs. They look/feel/smell like dual-linked ALSs and certainly perform like them in terms of eliminations. I'm slowly looking at over 1200 of these things just from the royle17 collection and I have thousands more from other collections. I guess these are what you call rank-0 structures?

I haven't even nailed down the elimination rules, although I'm working on the assumption that they are similar to standard dual-linked ALSs, and so far that's working. But, my engine is not finding all the potential eliminations as identified by Allan Barker's Xsudo during analysis of the involved sets/link-sets, so there's lots of room for exploration here.

So, is that what I see or have in mind? I guess the answer is that I'm not exactly sure where this is going, but it's been fun so far...

Cheers,

Paul

And as usual, code/executables have been refreshed with the latest dual-link DB code if anyone wants to play in my sandbox.

Paul

Rank 0 : a term which I first came across in Allan Barker's work. An excellent word.

Rank 0 structure just means any identified sudoku figure that has Rank 0.

All of the most interesting structures would appear to have Rank 0 since every link-set is a potential source of eliminations, so the more (link-sets in a Rank 0 structure), the merrier.

The two most prominent Rank 0 structures being Nice Loops and Dual-linked ALSs (DL- ALS).

I have to admit that I really don't know what to make of what I've called Type 1 DBs. They look/feel/smell like dual-linked ALSs and certainly perform like them in terms of eliminations

They are DL-ALSs !

Because you generate a second RCD through the stem cell or blossom or outside link or whatever it is called.

Just to remind ourselves : x is an RCD when x cannot be true in both ALSs (it may be false in both, but cannot be true in both, in other words they are weakly-linked).

Suppose now that A and B are singly linked ALSs : easily shown that this is a Rank 1 structure.

Then if we can find a candidate p in ALS A and a candidate q in ALS B such that p (all instances thereof) and q (all instances thereof) are weakly linked, then we have a second dual link, and so the structure has suddenly been radically improved into a Rank 0 structure.

In your structure, you find an outside stem (p,q) such that if p is true in ALS A then via the stem q is false in ALS B=>p and q are weakly linked=>second RCD=>dual-link=>Rank 0=>good news.

eg in your second example : p=7 {r4c9}, q=6 {r6c9} stem (p,q)=r3c9.

So the whole idea of searching for a second weak link is of the greatest interest.