X-Cycles alternating weak and strong links

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X-Cycles alternating weak and strong links

Postby ptsolver » Thu Jan 02, 2020 8:10 am

When digging in to the X-Cycles strategy, most places seem to talk about requiring alternating weak and strong links.

For example SudokuWiki says at https://www.sudokuwiki.org/X_Cycles

Strong and Weak links alternate just as candidates are turned OFF and ON. When we turn a candidate X ON we effectively remove ALL other candidates of X in ALL other units. However, when we turn a candidate X OFF it has no effect unless the unit has only two of X in it.


But if we look at the following board (https://www.sudokuwiki.org/sudoku.htm?b ... 0000005700) (link seems to be broken, trying to find another example) there's an X-Cycle.

X-Cycle
X-CYCLE on 1 (Discontinuous Alternating Nice Loop, length 8):
+1[G2]-1[G6]+1[E6]-1[F5]+1[F7]-1[C7]+1[C2]-1[G2]
- Contradiction: When G2 is set to 1 the chain implies it cannot be 1 - it can be removed


But the link G6 is a strong link to E6. Then E6 is marked as a weak link to F5 - though it seems like this is actually a strong link. Thus there a strong link between G6, E6, F5, and F7. The links F7 -> C7 and G2 -> G6 are evidently weak links, but i'm confused as to the actual requirements behind X-cycles requiring alternating types of links.
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Re: X-Cycles alternating weak and strong links

Postby ptsolver » Fri Jan 03, 2020 11:08 pm

Fixed link for the example above can be found at [url]https://www.sudokuwiki.org/sudoku.htm?bd=003158000090070080008002005100500000002030400300007008900400800830769010000005700[url]
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Re: X-Cycles alternating weak and strong links

Postby SpAce » Fri Jan 03, 2020 11:12 pm

ptsolver wrote:When digging in to the X-Cycles strategy X-Chain technique, most places seem to talk about requiring alternating weak and strong links.

No. You don't need alternating links, but you do need alternating inferences. Links are what exist in the grid, and inferences are how they're used in a chain. Weak links can only be used for weak inferences, but (native) strong links can be used in either role. That's why you can have a perfectly alternating inference chain (AIC) even if all the links are strong.

In general, don't believe everything you read on SudokuWiki. A lot of the terminology and information there is obsolete or crappy to begin with. I know because I started my studies there too, and it took a while to sort out all of the cognitive dissonance it caused. Unlearning is more difficult than learning. Use Hodoku. It's not perfect either but at least it's much better.
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Re: X-Cycles alternating weak and strong links

Postby ptsolver » Fri Jan 03, 2020 11:25 pm

SpAce wrote:You don't need alternating links, but you do need alternating inferences


I see! I think splitting out the link from the inference is really useful to think about. A seemingly strong link between two cells is being used to form a weak link if you're using it to infer A => !B.

but (native) strong links can be used in either role.

Just to dig in on terminology here, what's a non-native strong link in this context of chaining? It didn't feel super clear from the definitions i could find.
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Re: X-Cycles alternating weak and strong links

Postby eleven » Fri Jan 03, 2020 11:36 pm

ptsolver,

I can't see anything wrong in the SudokuWiki citation as well as in the nice loop.
You just have to know, that a "strong" link also can work as a "weak" link naturally:

"When we turn a candidate X ON we effectively remove ALL other candidates of X in ALL other units" (weak link to all these candidates)
A strong link just has one candidate to turn off, but it does, so it also has a weak link to it.
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