Quick Questions
Is this the simplest test for unconditional life? [#9064]
Hey guys, I am a beginner. I made up what I think is the simplest way to tell if a group is unconditionally alive. I think it's correct, but I haven't seen anyone else use it. Here it is:
A group is unconditionally alive if and only if each of its chains is touching at least two eyes which are being touched only by the group.
This is obvious for chains with two true eyes, since there is only one chain in the group, and that chain is completely surrounding two eyes, and therefore the eyes are being touched only by the group.
This also works for groups with only false eyes, such as the two-headed dragon or several of the shapes here (![[ext]](images/extlink.gif)
https://senseis.xmp.net/?SmallestGroupWithTwoEyes).
Am I correct in thinking that my definition is (1) correct, (2) not already somewhere on this site, and (3) the simplest way to test unconditional life?
Well, you would need to define what is an eye first, which is not actually as simple as it sounds. See Formal Definitions of Eye. But other than that, you're somewhat close to Benson's Definition Of Unconditional Life, so props for that.
My definition of an eye is a single empty space with a same-colored stone on all four sides. A true eye is when these four stones are part of the same chain, and a false eye is when they are not all part of the same chain.
Those might not be the standard definitions, but in the few games that I've played, they have been extremely helpful in keeping things simple and preventing confusion.
Also, thank you for your reply! You're right. After posting, I found Benson's definition, and mine looks like a narrower version of it. I think mine is less predictive because it doesn't comment on larger eye-spaces. So I guess my definition can say for sure that a given group IS unconditionally alive, but it can't say for sure that a group ISN'T unconditionally alive.
After additional reflection, I realize that I need to further attenuate my definition's power. It is merely a sufficient condition for unconditional life. If a group fits the definition, then it is unconditionally alive. But there are unconditionally alive groups that don't fit the definition (which means it needs revising):
![[Diagram]](diagrams/3/a73cc1377860df6bb51d82d9d39390da.png)
Obviously, to include the above group, I can't simply redefine an eye to be a connected region of empty spaces orthogonally surrounded by stones of only a single color, because then the definition would also include this group:
![[Diagram]](diagrams/8/17f8aae9c7fe88bf3186fb33244246ab.png)
You are trying to reeinvent the wheel making the standard mistakes of not defining "eye" and trying to define "one eye" before "two eyes". Unless you mean Benson-alive or pass-alive (you would not mean n-eye-alive), inform yourself about two-eye-formation.
Thank you for your reply. You're right. I will check out these resources!
Last night I realized that instead of using an "eye", it's better to use what I call a "secure territory". In my definition, a secure territory is one of two things: (1) a region of any number of connected empty spaces, which is surrounded by a single chain, and possibly containing enemy stones, or (2) a single empty space with a same-colored stone on all four sides, but not all four stones are part of the same chain.
If I take my previous definition and replace "eye" with "secure territory", then I think the definition now includes more options, without including that one above (that picture which I said should NOT be included).
I fixed the page I created, as far as I can tell.
It seems that being "vital" implies being "small". So couldn't Benson's definition be shortened to: "A group is unconditionally alive if and only if every chain touches at least two regions of which every space touches that chain." ?
Correction: "A group is unconditionally alive if and only if every chain touches at least two regions that are enclosed by the group, and of which every space touches that chain." ?
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