The New Sudoku Players' Forum

[daj95376]

bat999

We're opening an old disagreement here.

First, there's Eureka notation and, second, there's it's use to express AICs. They are not equivalent. Eureka notation can be used to express networks and non-AIC chains as well.

When Myth Jellies introduced AICs in 2006 ...

Alternating Inference Chain (AIC) is a chain which starts with an endpoint candidate which has a strong inference on the next candidate, which has a weak inference on the next candidate, which has a strong inference on the next candidate, and so on alternating weak and strong inferences until it ends with a strong inference on the final candidate at the other endpoint. The nodes of an AIC are really just the candidate premises themselves.

In the following inference definitions, A and B are candidates (or candidate premises).

I later participated in a disagreement on whether or not chains that start and end with a weak link were also AICs. Those who argued that they were AICs must have contributed to the Sudopedia entries on Eureka notation and AICs. Does that make it so? Not for me.

When it comes to AIC loops, he only references continuous loops ... and seems to discount Discontinuous Loops ... probably because they can be truncated to shorter AICs.

Deductions
Quite simply, at least one or the other (possibly both) of the two endpoint candidates (or candidate premises) of an AIC is true. Any deductions that you can make based on that are valid. This tends to produce the best results if the endpoints either share a group, or if the endpoints involve the same candidate. When your chain endpoints satisfy one of those conditions, it is time to check for any deductions.

If the two endpoints candidates are weakly linked, then you have an AIC loop. In this case, you could cut the loop at any weak link and end up with a valid AIC. Thus, for every weak link in the loop, either one or the other of the candidates joined by that weak inference are true, and you can make all appropriate deductions based on that.

That is pretty much all you need.

Here is an example that he included:

Code: Select all

 pure bilocation loop:
 *--------------------------------------------------*
 | 7    58   1    | 2    3    9    | 6    4    58   |
 | 6    38   2    | 1    4    5    | 389  89   7    |
 | 35   4    9    | 8    6    7    | 23   1    25   |
 |----------------+----------------+----------------|
 | 4   A123  38   | 369  5   B136  | 289  7    289  |
 | 9    235  357  | 37   8    34   | 24   6    1    |
 |E18   6    78   | 79   2    14   | 489  5    3    |
 |----------------+----------------+----------------|
 | 35   9    356  | 36   1    8    | 7    2    4    |
 |D128  13   368  | 4    7   C236  | 5    389  89   |
 | 28   7    4    | 5    9    23   | 1    38   6    |
 *--------------------------------------------------*
 A1=B1-B6=C6-C2=D2-D1=E1 (-A1)

Eureka notation
(1)r4c2 = (1-6)r4c6 = (6-2)r8c6 = (2-1)r8c1 = (1)r6c1...


Which I would write as:

1r4c2 = (1-6)r4c6 = (6-2)r8c6 = (2-1)r8c1 = 1r6c1 - loop


Bottom Line: Stop writing AIC next to your chains!

_

[DonM]

...Therefore, with Eureka AIC notation, discontinuities are never expressed as a loop ie. the weak link at both ends of the chain are NOT notated...

Hi
Sudopedia explains using Eureka notation with AICs here ---> http://sudopedia.enjoysudoku.com/Eureka.html
The final example on the page is:
(1)r5c4-(1=4)r5c8-(4)r9c8=(4-1)r7c7=(1)r7c4-(1)r5c4 => r5c4<>1

That is an error. If you were able to view virtually all the notated AICs on the Eureka forum (now sadly deceased) from 2007-2012 you would never see a chain like the above notated that way. For that matter, that has been true here when the solver is familiar with the correct Eureka format.

[bat999]

...Bottom Line: Stop writing AIC next to your chains!

OK
Let the reader figure out that it's merely a chain being used to arrive at a conclusion.
Not necessary to specify that it's an AIC or a Nice Loop or a Skyscraper or a *-Wing or whatever.

Code: Select all

.-----------------.-------------------.-----------------.
|  2    4     7   |  3     6     5    |  9     1    8   |
|  6    5     3   |  1     89    89   |  2     7    4   |
|  8    9     1   |  4     7     2    |  35    6    35  |
:-----------------+-------------------+-----------------:
| b35   267   8   |  9    c23    367  | b357   4    1   |
| 1     67   g59  | h57    4     3678 | a35-7  389  2   |
| 359   27    4   |  257   238   1    |  6     389  359 |
:-----------------+-------------------+-----------------:
| 59    1     6   |  8    d2359  39   |  4     239  7   |
| 4     3    f29  | e27    1     79   |  8     5    6   |
| 7     8     259 |  6    d2359  4    |  1     239  39  |
'-----------------'-------------------'-----------------'

(7)r5c7 - (7=35)r4c17 - (3=2)r4c5 - (2)r79c5 = r8c4 - (2=9)r8c3 - (9=5)r5c3 - (5=7)r5c4 - (7)r5c7 => -7 r5c7; stte

[ronk]

Be aware that Type 1 and Type 2 Discontinuous Loops can be expressed using Eureka notation, but most people choose to express the eliminations using shorter/equivalent Eureka notation for an AIC.

I assume you are using Jeff's assignment of Type numbers for nice loops. I've spent at least a half hour trying to find that seminal post ... without success. Would you please help me out?

[DonM]

Daj: 'First, there's Eureka notation and, second, there's it's use to express AICs. They are not equivalent. Eureka notation can be used to express networks and non-AIC chains as well.'

Near as I could tell, you're post was giving the background, as per Myth Jellies, for the substance of my post. However, I'm a little concerned that the above statement might be misunderstood though I understand what you're trying to say.

Here's the way I would describe what appears to be the distinction you're making:
The English language has a simple sentence core structure: Noun->Verb->Object. But, as we all know, in practice, the core is changed, sometimes drastically as various nuances and exceptions for dramatic purposes etc. are inserted.

The 2 basic forms of AICs as notated by the Eureka notation have been mentioned above. As solutions became more innovative and complex after 2006, the Eureka notation also evolved, albeit sometimes not perfectly, but enough that a reasonable consensus was arrived at for most structures including some of the most complex networks posted by solvers like SteveB and ttt. But no matter, what the structure, the core logic was alternating inferences ie. AIC structure, even if snippets of chains are being used.

I agree with you that there is no reason to designate a chain as an AIC when presenting a solution. First, there is no other notation being used and second, it infers that the chain being presented is some sort of unique structure. Besides, in practice -though a generalization- I think it has always been accepted that, in general, whether simple discontinuous chains, continuous loops, networks or whatever, they are all loosely referred to as AICs since the underlying structure is virtually always alternating inference chain snippets. That may not have have been the case when the Eureka notation was first being constructed, but it's been the case in every solving situation I've participated in since.

Finally, regarding the arguments you had with some on this subject: There have always been outliers that want to argue all sorts of minutiae and semantics with subjects like this. And there are always, luckily few, that are determined to see, and notate, things their own way regardless of how much it contributes to confusion in a sudoku solving forum.

[DonM]

...Bottom Line: Stop writing AIC next to your chains!

OK
Let the reader figure out that it's merely a chain being used to arrive at a conclusion.
Not necessary to specify that it's an AIC or a Nice Loop or a Skyscraper or a *-Wing or whatever.

Okay, I'll repeat: There is only a Nice Loop in Nice Loop notation; there is no such thing as a Nice Loop in Eureka notation. But, there is a continuous loop. I think you've become confused by referring to that other site that gives a tutorial on Nice Loops and are now transferring that information to use here.

Also, one doesn't make a distinction between an AIC and a Skyscraper or a *-Wing. The last two are structures which are (usually) notated within an AIC (Labels can be helpful to let the reader know what structure is being notated). Essentially, the AIC or snippets thereof, are the core of virtually all structures that are notated. (Although, it is okay to simply designate the parameters of something like an xy-wing without using alternating inferences.)

[daj95376]

Be aware that Type 1 and Type 2 Discontinuous Loops can be expressed using Eureka notation, but most people choose to express the eliminations using shorter/equivalent Eureka notation for an AIC.

I assume you are using Jeff's assignment of Type numbers for nice loops. I've spent at least a half hour trying to find that seminal post ... without success. Would you please help me out?

bat999 referenced a website listed in the "Collection of Solving Techniques" for Nice Loops.

It lists the Type 1/2/3 Discontinuous Loop definitions that we've been using.

Here is Jeff's thread on Forcing Chains. Note: I was in a discussion where the definition/properties of a forcing chain differed due to an alternative to Jeff's thread. I don't recall where to find the alternative. It may have been Sudopedia.

_

[ronk]

bat999 referenced a website listed in the "Collection of Solving Techniques" for Nice Loops.

It lists the Type 1/2/3 Discontinuous Loop definitions that we've been using.

Here is Jeff's thread on Forcing Chains.

Thanks daj95376, but neither matches the post I remember. Perhaps that's the problem, the memory.

[eleven]

Code: Select all

+-------------------+-------------------+-------------------+
| 2     4     7     | 3     6     5     | 9     1     8     |
| 6     5     3     | 1     89    89    | 2     7     4     |
| 8     9     1     | 4     7     2     | 35    6     35    |
+-------------------+-------------------+-------------------+
| 35    267   8     | 9     23    367   | 357   4     1     |
| 1     67   *59    |*57    4     3678  | 37-5  389   2     |
| 359   27    4     | 25-7  238   1     | 6     389   359   |
+-------------------+-------------------+-------------------+
| 59    1     6     | 8     2359  39    | 4     239   7     |
| 4     3    *29    |*27    1     79    | 8     5     6     |
| 7     8     25-9  | 6     2359  4     | 1     239   39    |
+-------------------+-------------------+-------------------+

This 4-cell bivalue loop jumps into the eyes:
5r5c3->7r5c4->2r8c4->9r8c3->5r5c3 => r5c7<>5,r6c4<>7,r9c3<>9

@Bat: if you write it as an AIC, you can easily see the eliminations.

[bat999]

...@Bat: if you write it as an AIC, you can easily see the eliminations.

Code: Select all

+-------------------+-------------------+-------------------+
| 2     4     7     | 3     6     5     | 9     1     8     |
| 6     5     3     | 1     89    89    | 2     7     4     |
| 8     9     1     | 4     7     2     | 35    6     35    |
+-------------------+-------------------+-------------------+
| 35    267   8     | 9     23    367   | 357   4     1     |
| 1     67   *59    |*57    4     3678  | 37-5  389   2     |
| 359   27    4     | 25-7  238   1     | 6     389   359   |
+-------------------+-------------------+-------------------+
| 59    1     6     | 8     2359  39    | 4     239   7     |
| 4     3    *29    |*27    1     79    | 8     5     6     |
| 7     8     25-9  | 6     2359  4     | 1     239   39    |
+-------------------+-------------------+-------------------+

5r5c3->7r5c4->2r8c4->9r8c3->5r5c3 => r5c7<>5,r6c4<>7,r9c3<>9

AIC: (9=5)r5c3 - (5=7)r5c4 - (7=2)r8c4 - (2=9)r8c3 => -9 r9c3
The trivial stream and the second stream together show only -9 r9c3 imho.

Don't we need to express the whole chain to see all the eliminations?
(Previous contributors in this thread have decided that this whole chain would not be an AIC)

(9=5)r5c3 - (5=7)r5c4 - (7=2)r8c4 - (2=9)r8c3 - (9=5)r5c3 => -5 r5c7, -7 r6c4, -9 r9c3; stte

It shows by reading the chain both ways that
the 5 will always be at either r5c3 or r5c4 in row 5 => -5 r5c7
the 7 will always be at either r5c4 or r8c4 in column 4 => -7 r6c4
the 9 will always be at either r5c3 or r8c3 in column 3 => -9 r9c3

omg, I think I have become a pedant too.

[eleven]

Don't we need to express the whole chain to see all the eliminations?

For a (closed) loop, i would do it, though in this simplest example you could derive the eliminations also from the shortened AIC.
Different to other AIC's in the loop all candidates on one side must be true and all on the other side must be false, while generally both may be true.