Mike Barker wrote:I finally got basic nice loops working (many other distractions and I still have to work on grouped nice loops

Congratulations Mike for a task well done.

Grouped nice loop can be implemented by simply adding a module for identification of links connected to grouped nodes.

Mike Barker wrote:I still had plenty of almost locked sets, poly-implication locked sets, and the usual number of uniqueness eliminations. The first and some of the second will be covered when I implement grouped nice loops.

Basically, all ALS rule patterns are discontinuous grouped xy-chains with strong nodes and pure links of weak inference. ALS patterns are poly-implication chains that won't be picked up by simple nice loop that covers double implication chains only. I am sure all ALS rule patterns will be picked up once grouped nice loop is implemented. In fact, grouped nice loop (of combined strong and weak types) should be much more powerful because it considers grouped nodes and links of strong and weak inferences. With the nice loop technique, almost patterns, uniqueness rectangles and BUG-Lites can be considered as a grouped node in the loop. Sometimes, a uniqueness rectangle can be considered as 2 cells with a link of strong inference in between.

Mike Barker wrote:The two remaining techniques, SueDeCoq and Empty Rectangles, occurred a handful of times each. SueDeCoq makes sense since it can link ALS with more than one extra candidate. Empty Rectangles appear to be in a catagory of their own. I wonder if there really aren't any other fish in that sea?

Each SueDeCoq is just 2 continuous grouped xy-chains. Empty Rectangles are just grouped x-cycles. They should be picked up once grouped nice loop is implemented.

Mike Barker wrote:On to grouped nice loops. Have you thought how the theorems might change for grouped nice loops? I'm thinking Theorm 1 will only go as far as stating "the node must be filled with one of the two digits that label the links".

So far, the grouped nodes that I have come across involve 2 links of weak inference or 2 opposite links. Good question; what would happen to a grouped node with 2 links of strong inference?

Mike Barker wrote:Theorems 2, 4 and 5 probably extend directly. I'm wondering if Theorem 3 might not reappear.

Theorem 2 extends directly with multi-eliminations when the link label is multi-valued. Theorems 3, 4 & 5 extend directly to grouped nice loop as long as the node at the discontinuity only has one cell.