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daj95376
Joined: 23 Aug 2008
Posts: 3854
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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 Posted: Mon Sep 29, 2008 9:11 pm Post subject: |
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[Edit to correct the previously erroneous explanation: the cells of an ALS must be peers.]
| daj95376 wrote: | | In the Players' Forums, udosuk uses a vwxyz-wing to perform [r2c1]<>2 -- the same elimination in my chain above. |
The same elimination, but not the same logic. (I already showed the AIC for daj's elimination, above.)
Those unfamiliar with the "vwxyz-wing" name might know it as a 2 ALS ("Almost Locked Sets", or n+1 candidates in n cells) elimination, of which it is just a particular instance. The very brief explanation of the elimination in the reference post might not be very clear for some.
| Code: | +----------------------+----------------------+----------------------+
|b1279 a27 1249 | 3 24579 2459 | 8 267 4567 |
| -278 5 248 | 6 2478 248 | 9 1 3 |
| 6 3 2489 | 2479 1 24589 | 24 27 457 |
+----------------------+----------------------+----------------------+
| 157 67 15 | 8 479 149 | 1346 3679 2 |
|b12 9 3 | 1247 6 124 | 5 8 47 |
| 4 2678 128 | 5 279 3 | 16 679 679 |
+----------------------+----------------------+----------------------+
| 2589 28 2589 | 29 3 6 | 7 4 1 |
|b239 1 6 | 249 2489 7 | 23 5 89 |
|b239 4 7 | 129 2589 12589 | 236 2369 689 |
+----------------------+----------------------+----------------------+ |
Here, ALS1 is the {27} bivalue in r1c2 (2 candidates in 1 cell). ALS2 is {12379} in r1589c1 (5 candidates in 4 cells). The "shared exclusive" digit is <7>, which can only occur in at most one of these two ALS, not both. (In logic terms, this means that there is a weak inference link between the <7>s of the two ALS.) The "shared common" digit is <2>. Because any 2 (grouped) digits within an ALS have a strong inference link, the grouped <2>s of each ALS work as pincer digits and eliminate <2> from any shared peer cells. The only such cells here are r23c1. And since r2c1 contains a <2>, it is eliminated.
The AIC is:
(2)r2c1 - (2=7)r1c2 - ALS[(7)r1c1=(2)r1589c1] - (2)r2c1; r2c1<>2
Last edited by Asellus on Tue Sep 30, 2008 9:44 pm; edited 1 time in total |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Sep 29, 2008 9:33 pm Post subject: |
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As to the technique name dispute, I agree with ravel's opinion (recently stated elsewhere here) that these arguments are largely pointless. As I see it, the meaning of terminology in sudoku is a living, evolving process, as with all language. Thus, it's as pointless to insist on some particular historical definitional aspect of a named technique as it is to, say, insist that "hopefully" is not a synonym for "I hope." Many techniques were noted independently and given different names and defined slightly differently. Different people picked up these names and, over time, they have merged and the original meanings expanded or been refined.
To me, the only thing that is useful is to focus on the underlying logic and object only when there is a critical logical difference which can lead to confusion and error if the uses of a name start to blur the difference.
Skyscrapers, (2-String) Kites and Turbot Fish, no matter to what particular patterns among them one considers each name to apply, all involve techniques that have identical underlying logic: 2 conjugate links connected by a weak link. There is no consistency as to which names various folks use for which patterns. Since they all have the identical logic, that's fine with me. (And, this pattern is the simplest form of the more general technique sometimes called "Color Wing," which describes two-cluster multicoloring with a weak "bridge" link. So, if someone calls a Skyscraper a Color Wing, that too is fine with me.)
As a counter example, ER eliminations and Kites/Turbot Fish do not have the same underlying logic and so should not be used interchangeably. While in the simplest and most common use of an ER (involving a single external conjugate link) the logic is very similar, an ER generally has a strong inference link (i.e., it is often not a conjugate link). So, not only is it not visually helpful (in leaning to spot them) to conflate the names, it obscures the underlying logical difference. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Oct 01, 2008 7:57 pm Post subject: |
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| Quote: | | helpful (in leaning to spot them) to conflate the names, it obscures the underlying logical difference |
conflate: to combine, to bring together.
again Asellus you have added another word to my vocabulary of an increasing list of interesting relevant sudoku terms.
and I totally agree that in order to form a more coherent understanding of the logic that is used in all techniques there should be some sort of diagram to go along with each name. that might take some of the confusion out of the discussion. that might also help people see the logic and therefore why its called a certain name in some instances and another name on other occasions. just my two cents.
its like the old picture of the two color Vase... some see a face, some see a Vase... I see a finned wing, someone else sees an ER. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed Oct 01, 2008 8:08 pm Post subject: |
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| storm_norm wrote: | again Asellus you have added another word to my vocabulary of an increasing list of interesting relevant sudoku terms.
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And I couldn't agree more with the content of Asellus' post!
Easy on the naming game, keen on structural differences.
-----
(I am very disappointed  that my suggestion of nunchuck as a common name for those two-strong-links-connected-by-weak-link patterns didn't find any followers). In the Daily Sudoku "
Do the June 4 Very Hard at the previous weekend!" thread I offered this altogether very sensible solution to the naming problem:
__________ (nataraj wrote:) _____________
And while I'm at it, might as well propose a NEW NAME (ta daa):
common name for x-wing, skyscraper, kite, turbot fish: NUNCHUCK
two rods (the strong links, made of wood I think) connected by a chain (the weak link). Every cell that gets into contact with the two buiness ends of the nunchuck loses a candidate.
Hashime.
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Oct 01, 2008 9:42 pm Post subject: |
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| Asellus wrote: | | As a counter example, ER eliminations and Kites/Turbot Fish do not have the same underlying logic and so should not be used interchangeably. |
I disagree. All three patterns are derived from Nick70's original pentagon patterns. Also, all three patterns can be expressed with identical-length, single-digit (NL) chains that all start with the assumption that a cell does not contain a specific digit. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Oct 01, 2008 10:31 pm Post subject: |
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nataraj,
Thanks for the kind words!
| daj95376 wrote: | | I disagree. |
Okay. But, it seems to me that you are rather missing my point. References to historic posts are interesting, but don't settle divergent terminological usages that have their own reasonable evolutionary histories, even if one doesn't agree with those usages. And geometric patterns are helpful mnemonics for learning and spotting techniques, but are not the same as underlying logic. Nor is the use of a forcing assumption relevent to the underlying logic.
ERs/Hinges and Kites/Turbot Fish/Skyscrapers have a different logical structure, even if their structures in certain limited instances are closely related. To see the difference requires making a clear distinction between conjugate links on the one hand and strong and weak inferences on the other. I will use the * symbol to represent a conjugate link, since I am unaware of any symbol agreed upon for that purpose. "=" and "-" represent strong and weak inferences, respectively.
All Turbot Fish/Kites/Skyscrapers have this structure:
Xv - X*X - X*X - Xv
two conjugate links joined by a weak inference, where Xv represents the victim(s).
The term ER/Hinge (as it is now used) doesn't really refer to a stand-alone technique per se. Rather, it refers to a structure that is used in conjunction with others. That alone makes it different. But, the logic also differs.
Some ER applications, the common basic sort, have this structure:
Xv - X*X - ER(X=X) - Xv
which is as close as an ER gets to a Turbot Fish. Even more, the use of the ER term and concept is not limited to this basic case. ERs, referred to as such, are very frequently used as part of a variety of solving situations (transporting a wing pincer or a "fish fin", for instance). As such, the general form of an ER is:
Xv - X = [intervening AIC/Wing optional] = X - ER(X=X) - [intervening AIC/Wing optional] - Xv
This is NO Turbot Fish! |
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