I've gained some good experience with it My main intension with that concept is to have a method for deciding whether a chain surrounds territory or not. (It depends a bit on the implementation / context whether it's decidable or just gives a necessary condition.)

To the idea (viewtopic.php?p=154283#p154283) about changing the definition of capturable-1, I've not considered that changing this definition would (maybe) change capturable-2, too. Idk if it matters, so I better use the term "alive-1" instead to keep the definitions constantly.
Alive(-n) and (un)capturable(-m) are independent concepts (and quite different for the x-2 case) but for the x-1 case they seem to be relative close.

My previous EfAJa model required that a chain is alive-1 to suround territory. (It works simular as the newest, but uses 3 different states for the confirmation of live and death instead only 2. A chain is either alive-1, alive-2 or dead, instead of either alive or dead.)
While it was true by definition there (that territory requires alive-1), now it's just a feature. After I found out that 2 states are enough I stopped to work on 3 and have not proved all equivalence conditions, but if this wouldn't be equivalent (in correct passed situations) I guess I would have a problem with at least one of them

Mixing with some terms from J2003, alive-1 contains all uncapturable, all capturable-1 and a subset of capturable-2. For the rules it doesn't matter how you *call* that chains but somehow a position like example0000 (from J2003) doesn't *look* like a 'normal' capturable-2...


Definitions:

For 'eye' I had more a low-level definition in mind instead of 'two-eyes'. I think probably both would work, but one eye is easier.

An intersection is an "eye-intersection" if:
* it is empty and
* it is adjacent to a stone and every adjacent intersection has the same color.

A chain is "alive-1" if: (at the end of the status-analysis for the chain)
- there is at least one stone on the chain (where the chain was before the analyse) or
- there is at least one eye-intersection on the chain.


Btw. for alive-1, instead of the 'at least one...', it's also possible to use the rule 'All intersections of the chain must be covered by either a stone or an eye-intersection of the defender.' What is better depends mainly on the other rules (and of corse the aim), but it makes surprisingly little difference ... so there is some freedom ... and possible combinations for study

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | . O O O . |
$$ | O O X O O |
$$ | O X , X O |
$$ | O O X O O |
$$ | . O O O . |
$$ +-----------+[/go]

Is tengen an eye for black?

Maybe you meant "it is adjacent to at most a single string" or something?

If so, the following black group would be without any eyes:

Click Here To Show Diagram Code

[go]$$B
$$ +-------------+
$$ | . O O O O O |
$$ | O O O O O O |
$$ | . O O O O O |
$$ | O O X X O O |
$$ | O O X . X X |
$$ | O O X X . X |
$$ +-------------+[/go]

edit: oh, guess this is about go rules wizardry and an eye-intersection has nothing to do with what I would call an eye? Carry on then.

Yea, that's why I used "eye-intersection"
*If* the analysis would be over in the first position then tengen would be a black eye-intersection, but of corse w would capture at tengen before ending the analysis...