Forum for Formal Definitions of Eye

moving Elroch's contribution here [#1205]

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Dieter: moving Elroch's contribution here (2007-11-19 21:48) [#4050]

A little warning for the more fussy

Elroch: The topic of eyes is somewhat confused by using a loose definition of what makes a "group" of stones. An eye may be defined as a set of points entirely surrounded by stones of the same colour. A solidly connected group (called a chain or string)benefits from an eye if it is in contact with it (two or more chains may be in contact with the same eye. A chain is alive if it is in contact with two eyes (with the proviso that if one of the two eyes contains a point not in contact with any stones in the group, there is a possibility of invasion which could kill the group or create a seki). These concepts are discussed in detail in Benson's algorithm.

"False eye" (actually a chain of three white stones in contact with only one eye that cannot be joined to the other group without destroying the eye)  

From this viewpoint what is known as a false eye is a chain that only has contact with one eye, and which may not be joined to the other chain forming the false eye in a way which leaves the new chain with two eyes.

Addition of a few white stones reveals the supposedly false eye to be fully functioning, and important for the survival of each of the two chains. Both white chains are unconditionally alive, with two eyes each, including one that is shared between them both. Hence the white group is unconditionally alive.  

The value of the idea of false eyes is to distinguish when two chains cannot be connected solidly without destroying an eye that is essential to life, but it must be remembered that such an eye can still be useful if all attached groups can acquire one more eye each.

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