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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Thu May 05, 2011 2:57 am    Post subject: Reply with quote
Quote:
(Z=X)cell_a - (X=Y)cell_b - (Y=Z)cell_c => elimination of Z in peers of cell_a and cell_c

Danny,

If you had said something like
Quote:
a(Z=X) - (X=Y) - b(Y=Z) ^ Z {a,b}
then, I'd think we are getting somewhere.

Keith
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Thu May 05, 2011 8:32 am    Post subject: Reply with quote
keith wrote:
Code:

+---------+---------+---------+
| .  /  . | .  .  . | .  .  . |
| .  aX . | . XYZ . | .  XY . |
| .  /  . | .  .  . | .  .  . |
+---------+---------+---------+
| .  /  . | .  .  . | .  .  . |
| .  /  . | .  .  . | .  .  . |
| .  /  . | .  .  . | .  .  . |
+---------+---------+---------+
| .  bX . | .  XZ . | .  .  . |
| .  /  . | .  .  . | .  .  . |
| .  /  . | .  .  . | .  .  . |
+---------+---------+---------+

...
Please write Marty's loop (edit:) as described by me (end edit) in the notation of your choice.

(X=Z)r7c5 - (ZY=YX)als:r2c58 - (X)r2c2 = (X)r7c2 - loop

Since it's a loop, a continuous loop in NL terms, all links become conjugate including the locking of digit <Y> in the ALS. This implies ...

r1345689c5<>Z, r2c134679<>X, r7c1346789<>X, r2c1234679<>Y

r2c2<>Y, which you missed, is called a "cannibalistic" elimination.

My notation of preference is NL notation, but it's apparently not used here. Smile [edit: rotate notation to locate ALS at or near the middle]

Last edited by ronk on Thu May 05, 2011 12:53 pm; edited 1 time in total
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu May 05, 2011 11:18 am    Post subject: Reply with quote
I'm still trying to understand Ron's ALS notation. However, I'm perfectly happy with a forcing chain based on Z in r2c5.

Code:
+---------+---------+---------+
| .  /  . | .  .  . | .  .  . |
| .  aX . | . XYZ . | .  XY . |
| .  /  . | .  .  . | .  .  . |
+---------+---------+---------+
| .  /  . | .  .  . | .  .  . |
| .  /  . | .  .  . | .  .  . |
| .  /  . | .  .  . | .  .  . |
+---------+---------+---------+
| .  bX . | .  XZ . | .  .  . |
| .  /  . | .  .  . | .  .  . |
| .  /  . | .  .  . | .  .  . |
+---------+---------+---------+

stream r2c5<>Z: (Z)r2c5 = (XY)r2c58 - (X)r2c2 = (X)r7c2 - (X=Z)r7c5

stream r2c5= Z: (Z)r2c5 - (Z=X)r7c5 - (X)r7c2 = (X)r2c2 - (X=Y)r2c8

Common eliminations:

Code:
r2c134679 <>X
r7c1346789<>X
r2c1234679<>Y
r1345689c5<>Z

In practice, since the streams are almost bidirectionally identical, I would use:

Code:
(Z=XY)r2c58 - (X)r2c2 = (X)r7c2 - (X=Z)r7c5 - loop

With the implied understanding that following the loop from right-to-left will have my second stream as its particulars.

Regards, Danny
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Thu May 05, 2011 8:06 pm    Post subject: Reply with quote
Ron and Danny,

Thank you.

It's all German to me: A language I can read well enough, but I cannot write! Smile

A thing that bothers me, and I am not picking on anyone, is that the notation is full of references to specific cells in the grid. You can rotate the puzzle, or (to some extent) move lines (columns or rows) around. The logic is unchanged, but the expressions have to be rewritten. I can think of some ways to reduce the references to specific cells, but not to eliminate them.

ronk wrote:
Quote:
r2c2<>Y, which you missed, is called a "cannibalistic" elimination.
Yes, I have edited the original post to note that, and also to correct an error.

I have noticed such a thing before, particularly with M-wings. An elimination is made in one of the cells that forms the chain.

I suppose the ultimate cannibal is a Type-4 UR, where the elimination destroys (or at least obscures) the original pattern. It can also happen with coloring, that the elimination solves (and destroys) the chain. Maybe that is a "suicidal" elimination? Smile

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Thu May 05, 2011 9:26 pm    Post subject: Reply with quote
I haven't been able to follow this thread. Last week I had a cell, XY, from which I started an XY-Chain. The X "proved" Y in the same cell, so naturally I eliminated X. Is that a cannibalistic elimination?
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Fri May 06, 2011 1:40 am    Post subject: Reply with quote
keith wrote:
It's all German to me: A language I can read well enough, but I cannot write! Smile
...

I can think of some ways to reduce the references to specific cells, but not to eliminate them.

If the result is similar to some of the other "chains" you've written ... it would likely be a Greek I could't even read. Smile

keith wrote:
I have noticed such a thing [ronk edit: a cannibalistic exclusion] before, particularly with M-wings. An elimination is made in one of the cells that forms the chain.

I can't imagine how a cannibalistic exclusion might occur with a simple m-wing. Please point me to an example.

Marty R wrote:
I haven't been able to follow this thread. Last week I had a cell, XY, from which I started an XY-Chain. The X "proved" Y in the same cell, so naturally I eliminated X. Is that a cannibalistic elimination?

For a cannibalistic exclusion, the X has to be used as a member of a strong-inference-set. From what you describe, I suspect the X was weakly linked to both the "next cell" in the XY-chain and the Y at the other end of the chain. As such, it would not be cannibalistic.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri May 06, 2011 3:04 am    Post subject: Reply with quote
ronk said:
Quote:
I can't imagine how a cannibalistic exclusion might occur with a simple m-wing. Please point me to an example.

I'll have to look.

Keith
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