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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Mon Apr 26, 2010 9:28 pm Post subject: AIC question |
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I feel silly asking this, but those of you who know me know I'm not much of a theorist, and this question has been on my mind. I'm just curious, I have no specific situation that spawned this question.
Are all chains AICs? I can't think of a good antonym for "alternating", but are there chains whose inferences can be strong-strong-strong or weak-weak-weak? What about things like simple coloring, remote pairs or XY-Chains? What kind of chains are they? |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Apr 29, 2010 4:25 pm Post subject: Re: AIC question |
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| Marty R. wrote: |
Are all chains AICs? I can't think of a good antonym for "alternating", but are there chains whose inferences can be strong-strong-strong or weak-weak-weak? What about things like simple coloring, remote pairs or XY-Chains? What kind of chains are they? |
Simple Colouring, XY Chains and remote pairs can all be represented as AICs.
I too am not a great theorist but the following might help - reasonably well written - especially the section on discontinuous Nice Loops.
http://www.paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 30, 2010 3:43 am Post subject: |
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Thanks MM.
| Quote: | | Simple Colouring, XY Chains and remote pairs can all be represented as AICs. |
If this is true, then I assume that there are no chains that are strong-strong-strong or weak-weak-weak. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Apr 30, 2010 5:11 am Post subject: |
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Thats why I directed you to Nice Loops - especially the bit on discontinuities.
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Fri Apr 30, 2010 5:38 am Post subject: |
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| Marty R. wrote: | Thanks MM.
| Quote: | | Simple Colouring, XY Chains and remote pairs can all be represented as AICs. |
If this is true, then I assume that there are no chains that are strong-strong-strong or weak-weak-weak. |
I am probably lost, I thought all strong links may be considered weak. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Apr 30, 2010 6:50 pm Post subject: |
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| wapati wrote: | | Marty R. wrote: | Thanks MM.
| Quote: | | Simple Colouring, XY Chains and remote pairs can all be represented as AICs. |
If this is true, then I assume that there are no chains that are strong-strong-strong or weak-weak-weak. |
I am probably lost, I thought all strong links may be considered weak. |
wapati, that is a common misconception. It is NOT true.
strong link means "at least one of the statements must be true"
weak link means: "at most one of the statements is true"
those two are not the same.
In simple cases (most strong links we find at first), like exactly two cells with candidate "6" in a row), there is both a strong link (at least one of the cells must be "6") and a weak link (only one of them can be "6") but in the general case, strong does not imply weak. Take the pincers of a w-link, for example. The w-link means that at least one of the pincers is "x". But it is possible that both are "x". Same with m-wing etc.
Chains of weak-weak or strong-strong are not particularly useful.
Why?
strong link can also be written as: "if not a then b"
weak link can be written as: "if x then not y"
put those together and you get something new (=better) from the original links:
(if not a then b) and (if b then not c) and (if not c then d) gives: if not a then d. This new relationship can be useful.
two strong links cannot be put together to form a useful new relationship:
(if not a then b) and (if not b then c) do not connect in a useful way
neither can we combine two weak links:
if a then not b and if b then not c does not tell us anything about the relationship between a and c. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Fri Apr 30, 2010 11:18 pm Post subject: |
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| wapati wrote: | | Marty R. wrote: | Thanks MM.
| Quote: | | Simple Colouring, XY Chains and remote pairs can all be represented as AICs. |
If this is true, then I assume that there are no chains that are strong-strong-strong or weak-weak-weak. |
I am probably lost, I thought all strong links may be considered weak. |
I believe you're thinking of a conjugate link, which has both a strong inference and a weak inference. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sat May 01, 2010 12:11 am Post subject: |
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| ronk wrote: |
I believe you're thinking of a conjugate link, which has both a strong inference and a weak inference. |
Thank you. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat May 01, 2010 6:47 pm Post subject: |
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[Withdrawn: Probably of little use to Marty.]
Last edited by daj95376 on Sat May 01, 2010 11:20 pm; edited 1 time in total |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat May 01, 2010 8:51 pm Post subject: |
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| daj95376 wrote: | | Asellus and ronk are more apt to use an AIC based on (N+1) WIs connected to N SIs. In this case, listing eliminations is redundant because it's a contradiction chain/discontinuous loop where the assumption in the initial WI is disproven by the conclusion in the final WI. |
To be clear, there's no more and no less assumption involved in writing the deduction as a loop ... rather than a chain. Moreover, without a loop there is no deduction. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sat May 01, 2010 10:40 pm Post subject: |
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| Without being disrespectful to anyone - does this help at all Marty ? |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun May 02, 2010 12:03 am Post subject: |
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| Mogulmeister wrote: | | Without being disrespectful to anyone - does this help at all Marty ? |
I don't want to seem like an ingrate to all who responded, but if my basic question was answered, I missed it. Sorry, but a lot of theory discussion is Greek to me.
| Quote: | | ...but are there chains whose inferences can be strong-strong-strong or weak-weak-weak? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 02, 2010 2:02 am Post subject: |
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| Marty R. wrote: | | Quote: | | ...but are there chains whose inferences can be strong-strong-strong or weak-weak-weak? |
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Not to my knowledge. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun May 02, 2010 4:47 am Post subject: |
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| daj95376 wrote: | | Marty R. wrote: | | Quote: | | ...but are there chains whose inferences can be strong-strong-strong or weak-weak-weak? |
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Not to my knowledge. |
Thanks very much Danny. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun May 02, 2010 7:38 am Post subject: |
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| Quote: | | but are there chains whose inferences can be strong-strong-strong or weak-weak-weak? |
Well yes, if you change the candidates. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun May 02, 2010 1:37 pm Post subject: |
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| over and out. |
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