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 leeo
 Joined: 24 Jun 2009  Posts: 6  :  Location: USA NW  Items 

Posted: Fri Aug 21, 2009 12:59 pm Post subject: Re: Documenting Nice Loops and Chains 


daj95376 wrote: 
I'm accustomed to working with chains and rarely rely on loops 

They are, of course, the exact same concept, and yes, from the persepective of chains, the "loop" notation is extraneous. I started with the following very lucid artice [look up "nice loops in sudoku", this board does not permit me to post the link], which did give me a "loopy" perspective.
This does suggest one idea for improvement: search through the building chain for all "cross innersection" moves. These can be expressed as loops, but it then does make it easier to find elimination moves. 

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 nukefusion
 Joined: 27 Jun 2009  Posts: 22  :   Items 

Posted: Wed Sep 09, 2009 12:05 pm Post subject: 


Ok, I wonder if anyone can help here.
If I'm understanding everything correctly, any nice loop can be represented by an equivalent AIC.
Take this nice loop example below. Can anyone please tell me what the equivalent AIC is? I've got stuck trying to figure it out.
Last edited by nukefusion on Wed Sep 09, 2009 6:25 pm; edited 1 time in total 

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 daj95376
 Joined: 05 Feb 2006  Posts: 349  :   Items 

Posted: Wed Sep 09, 2009 4:50 pm Post subject: 


Your puzzle can be solved with singles, but you stopped halfway through to ask about a chain that doesn't make any sense to me.
Would you please list and explain the individual connections! 

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 nukefusion
 Joined: 27 Jun 2009  Posts: 22  :   Items 

Posted: Wed Sep 09, 2009 5:14 pm Post subject: 


daj95376 wrote:  Your puzzle can be solved with singles, but you stopped halfway through to ask about a chain that doesn't make any sense to me.
Would you please list and explain the individual connections! 
I'm kind of glad it doesn't make any sense to you, because it doesn't make sense to me either.
This example of a nice loop is generated by a piece of software you can download from the internet. Using it you can view all of the available steps, at any given time. I realize the puzzle itself can be solved using just singles, but nevertheless this nice loop, according to the software, is valid and available immediately after you open the puzzle (regardless of whether it would ever be useful in real life).
So I guess that's my question, is it valid? And if so, how does it translate into an AIC, because I couldn't work it out (which kind of puts a damper on the understanding I thought I had about AIC's) 

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 daj95376
 Joined: 05 Feb 2006  Posts: 349  :   Items 

Posted: Wed Sep 09, 2009 9:14 pm Post subject: 


I think that I've manged to understand what it's doing.
I hope you understand Eureka notation because I don't use NL notation anymore.
Code:  **
 1468 3 7  2 58 9  68 1456 146 
 1468 9 145  158 578 1378  368 2 13467 
 18 158 2  4 6 1378  389 13579 1379 
++
 2 8 9  5689 1 4  7 369 369 
 3 7 149  69 29 2  5 8 2469 
 5 6 49  3 2789 278  1 49 249 
++
 7 1245 8  19 249 6  239 139 1239 
 19 12 6  19 3 5  4 179 8 
 149 124 3  7 2489 128  269 169 5 
**

Here's the chain as a discontinuous nice loop in WIbased AIC. It makes all of the arrows point at each other.
Code:  (2)r7c2  (2=1)r8c2  (1=9)r8c1  (9=1)r8c4  (1=2)r8c2  (2)r7c2; => r7c2 <> 2
_______________________________________________________________________________

I prefer to use the SIbased AIC. It translates into the <19> Naked Pair elimination.
Code:  (1=9)r8c1  (9=1)r8c4 ; => r8c2 <> 1
_______________________________________________________________________________

Bottom Line: Always perform basic techniques before searching for a chain! 

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 nukefusion
 Joined: 27 Jun 2009  Posts: 22  :   Items 

Posted: Thu Sep 10, 2009 6:05 am Post subject: 


Thanks for your reply daj95376. I don't know what WI/SI is but I understand the notation.
Is it valid to reuse the candidates 1/2 in R8C2 at another point in the loop? I think that's what has caused my confusion here. 

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 PIsaacson
 Joined: 17 Jan 2006  Posts: 47  :  Location: Campbell, CA  Items 

Posted: Thu Sep 10, 2009 6:34 am Post subject: 


nukefusion wrote:  Is it valid to reuse the candidates 1/2 in R8C2 at another point in the loop? 
Not with nrc chains. The prior conjugate pair strong link (2=1)r8c2 prohibits the later conjugate pair strong link (1=2)r8c2. This produces an nrc whip which basically states that any prior "truth" (right hand side of the conjugate pairs) cannot be contradicted by some later discovered truth. I've never seen niceloops implementations that take advantage of this, mainly because of the reversibility problem. If you consider prior "truths" during chain generation, then you obviously get into conditions where the chain quickly becomes nonreversible. That's why nrc chains don't have anything equivalent to continuous loops.
Cheers,
Paul 

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 daj95376
 Joined: 05 Feb 2006  Posts: 349  :   Items 

Posted: Thu Sep 10, 2009 4:14 pm Post subject: 


PIsaacson wrote:  nukefusion wrote:  Is it valid to reuse the candidates 1/2 in R8C2 at another point in the loop? 
Not with nrc chains. The prior conjugate pair strong link (2=1)r8c2 prohibits the later conjugate pair strong link (1=2)r8c2. This produces an nrc whip which basically states that any prior "truth" (right hand side of the conjugate pairs) cannot be contradicted by some later discovered truth. I've never seen niceloops implementations that take advantage of this, mainly because of the reversibility problem. If you consider prior "truths" during chain generation, then you obviously get into conditions where the chain quickly becomes nonreversible. That's why nrc chains don't have anything equivalent to continuous loops.

My answer is in addition to what Paul wrote.
The biggest problem I had/have with chains is that they are not suppose to have a "memory" of previous eliminations in the chain. Otherwise, they're a network. However, this lack of "memory" doesn't apply to cells being visited. Otherwise, infinite loops would exist.
(Does this qualify as an oxymoron?)
Being a WIbased AIC and a discontinuous nice loop, is what makes this chain appear to be unorthodox, IMO.
Some definitions and history.
Code:  SI: Strong Inference
WI: Weak Inference

When Myth Jellies introduced the AIC, it was based of an SI being first:
If you use his definition and elimination logic, then all you need is ...
Code:  (2=1)r8c2  (1=9)r8c1  (9=1)r8c4  (1=2)r8c2; => r79c2 <> 2
_______________________________________________________________________________

... and the loop stops when it returns to the same cell. At this point, eliminations can be derived.
(Note: there are two eliminations!)
Now, many people like to make the elimination(s) an obvious part of the chain. So, they turn the chain into a WIbased AIC by assuming that the eliminations are true at the front and concluding that they aren't at the end.
(I call this a contradiction chain  a very old name that's no longer used by others.)
Code:  (2)r7c2  (2=1)r8c2  (1=9)r8c1  (9=1)r8c4  (1=2)r8c2  (2)r7c2; => r7c2 <> 2
_______________________________________________________________________________

This lets a chain enter and leave a cell ... and to (sometimes) return later to enter and leave the same cell. This gives it the appearance of a whip, but I only use the term whip to imply a more complicated scenario. In the case of this chain, only one SIbased AIC elimination is initially assumed true ... and so only one elimination is derived as false.
I haven't used WIbased AICs in a long time, but I have recently been known to list them as an alternative view of my SIbased AICs.
Note: Since a WIbased AIC already starts and ends with the elimination cell(s), I consider the conclusion to be selfevident and often drop the (redundant) specific declaration of elimination(s).
Code:  (2)r7c2  (2=1)r8c2  (1=9)r8c1  (9=1)r8c4  (1=2)r8c2  (2)r7c2
_______________________________________________________________________________



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