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XY-Chain

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Aug 26, 2007 12:32 am    Post subject: XY-Chain Reply with quote

I asked this question in the middle of a thread on another forum, but didn't get a reply, so I'll try here.

Here's one definition:

"The XY-Chain technique is an extension of the XY-Wing technique where a chain of cells is formed. Each link in the chain is a pair of cells in the same unit that have two candidates each and share a common candidate."

How strictly do most of you adhere to this definition? Suppose there are one or more trivalue cells or other deviations from the definition. Do you still use the term XY-Chain or do you call it something else? I've used the term a couple of times when it deviated, and I'm wondering if I'm deceiving people.

Of course, I also wonder when I see others use the term if they're being strict or flexible with the definition.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun Aug 26, 2007 1:13 pm    Post subject: Reply with quote

When I use the term, the chain only involved cells that were bi-value before I started the chain. And, now that I think about it, I guess I assume that is the case when others use the term, but I suppose the only time I might even notice is if I tried to recreate your chain that way and couldn't do it.

However, I know that if you call your chain an XY-chain, even if doesn't strictly meet the definition, your intent is not to deceive but, by using a term and its implied logic that most will readily understand, to describe.

A question I have is, and I hope this is not the deviation Marty is talking about, if a cell becomes bi-value in the course of constructing the chain, can it be used and still considered an XY-chain?
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Aug 26, 2007 3:58 pm    Post subject: Reply with quote

Quote:
A question I have is, and I hope this is not the deviation Marty is talking about, if a cell becomes bi-value in the course of constructing the chain, can it be used and still considered an XY-chain?


Yes, that is one of the deviations I've come across, although I don't have any examples. On at least two occasions there have been two trivalue cells, say, 345-345. Earlier in the chain those cells became a naked pair, then the chain continued.

As to your question, I don't know if it's strictly an XY-Chain. But I've used the term when I've had a chain that produced the pincer effect, even if it didn't meet the literal definition.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sun Aug 26, 2007 5:43 pm    Post subject: Terminology Reply with quote

For want of any other choice, I propose we try to standardize on the terminology used in Sudopedia.

http://www.sudopedia.org/wiki/Terminology

At least you can edit it if you feel strongly enough!

Keith
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sun Aug 26, 2007 7:16 pm    Post subject: Reply with quote

If I include nodes with 2 or more cells in such a chain, I call it an "ALS Chain." To me, an XY Chain is just a special case of the more general ALS Chain since bivalue cells are the smallest possible ALS.

If I depart from ALS nodes by, for example, exploiting a strong link within a House somewhere along the chain, then I call it an AIC (Alternate Implication Chain), which is an even more general term. ALS Chains are a sub-type of AIC.
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