The New Sudoku Players' Forum

[DEFISE]

However, I basically know the argument of the AIC followers: AIC is not a "memory chain"

Except the AIC notation is also used to code "memory chains" and pretend they are something new.

if there is no 6 in r7c49, there must be (5 and) 4r7c9
then no 4 is in r3679c3, there must be (123 and) 5r6c3
then no 5 is in r5c1258, there must be (139 and) 6r5c5
=> either 6r7c4 or 6r5c5 (or both)

I don't know if there is memory or not, but to me this sounds more like T&E (moreover, with branching) than anything else.

In any case, it allowed me to understand this AIC, which looks like an anti-track P '(6r7c4), without the memory, precisely. A little nod to Robert Mauriès ...

Anyway it seems to me that eleven said somewhere on this site that he was not a big fan of AIC or at least of Eureka notation…

[mith]

However, I basically know the argument of the AIC followers: AIC is not a "memory chain"

Except the AIC notation is also used to code "memory chains" and pretend they are something new.

if there is no 6 in r7c49, there must be (5 and) 4r7c9
then no 4 is in r3679c3, there must be (123 and) 5r6c3
then no 5 is in r5c1258, there must be (139 and) 6r5c5
=> either 6r7c4 or 6r5c5 (or both)

I don't know if there is memory or not, but to me this sounds more like T&E (moreover, with branching) than anything else.

No branching involved here. Each strong link is just using an ALS - one end or the other must be true or you end up with 1 digit for 2 cells, or 3 digits for 4 cells. You could write the first link more clearly as a regular AIC - (6=5)r7c4 - (5=4)r7c9, for example (the others would have to be grouped using the 123 and 139 triples) - but the pattern is an ALS XY-wing so it makes sense (to me) to express it as an XY-wing with ALS nodes rather than splitting them. YMMV.

It's not hard to spot the individual ALS based links manually, though as eleven says you could end up checking a lot of these before finding some that work together, never mind finding the one (in this puzzle) that solves the puzzle. (And I certainly would find all the fish before resorting to something like this if I were solving manually.)

[eleven]

I don't know if there is memory or not, but to me this sounds more like T&E (moreover, with branching) than anything else.

It is as much T&E as any chaining technique. Looking at the almost locked sets (ALS) just provides you with more strong links (in addition to bivalue/bilocation), so you have more possibilities to build chains (with or without memory).
E.g. if you look at row 4 in this puzzle

Code: Select all

| 1279    4      6     |a12    3    b189    |c1789    5     a19  |

you can immediately see the strong links
2r4c4 = 9r4c9, then 2r4c4 = 8r4c6 and 2r4c4 = 7r4c7
(all useless here, because 2r4c4 cannot be expanded - and at the end turns out to be wrong).

Or in row 9 you have the links

Code: Select all

| 12389   5     b123   | 13    4     78     | 1379    6      139 |

2r9c3=9r9c9, 2r9c3=7r9c7

You will get the same, if in the chains (nodes) not only singles, but also subsets (pairs, triples, quads) are used.

[denis_berthier]

In any case, it allowed me to understand this AIC, which looks like an anti-track P '(6r7c4), without the memory, precisely. A little nod to Robert Mauriès ...

As anti-tracks are T&E(S) (possibly to levels 2 and more), it is not surprising that what is basically an S-braid (in this case, without z- or t-candidates) be covered by some anti-track. Sorry for Robert, but he didn't invent this wheel.

[denis_berthier]

I don't know if there is memory or not, but to me this sounds more like T&E (moreover, with branching) than anything else.

It is as much T&E as any chaining technique. Looking at the almost locked sets (ALS) just provides you with more strong links (in addition to bivalue/bilocation), so you have more possibilities to build chains (with or without memory).

All this is absolutely right. Having Subsets in chain patterns is a very old topic and unrelated to T&E. My remark about T&E was more influenced by Defise's remark about anti-tracks than by the citation of you I put above it; I understand it might have been confusing.

[denis_berthier]

However, I basically know the argument of the AIC followers: AIC is not a "memory chain"

Not exactly. "Memory chains" didn't exist at the time of AICs. "Memory chains" are a name invented much after to cover anything with z- and/or t- candidates without referring explicitly to them; as many things in Sudoku, it's so vague that it can include any contradiction chain.

At the time of AICs, the main argument for them was reversibility. I think it remains a very good argument for them. In my approach, several patterns are indeed reversible: bivalue-chains (the classical AICs), z-chains and Reversible Subset Chains (basically the AICs with inner Subsets). Strangely enough, for some reasons of their own, the same people who defended reversibility also hated z-chains.

This notion of reversibility, vague as it was, was so deeply entrenched in the approaches of the time that my introduction of non-reversible chains in [HLS, 2007], with z- and/or t-candidates, was unanimously attacked on the forums (then dominated by the AIC worshippers) as something directly escaped from Hell.

One problem with reversibility is defining it. (Still today, you can see people trying to explain reversibility in terms of De Morgan laws.) It had never been defined precisely before I did it in [CRT] and [PBCS], where I also proved that "Reversible Subset Chains" are indeed reversible in my precise sense.

The problem with Reversible Subset Chains (AICs with inner Subsets) is not their complexity; it is their lack of resolution power relative to their complexity. Whips of same global length have a much higher resolution power.

[eleven]

The problem with Reversible Subset Chains (AICs with inner Subsets) is not their complexity; it is their lack of resolution power relative to their complexity. Whips of same global length have a much higher resolution power.

Of course "memory chains" are more powerful than those, where you don't have to remember each elimination done on the way.

[denis_berthier]

The problem with Reversible Subset Chains (AICs with inner Subsets) is not their complexity; it is their lack of resolution power relative to their complexity. Whips of same global length have a much higher resolution power.

Of course "memory chains" are more powerful than those, where you don't have to remember each elimination done on the way.

In whips, no eliminations are "done on the way" - and one doesn't have to remember z- or t-candidates.
What I mean in the above comparison is, considering basics AICS (bivalue-chains), there are two ways of extending them
- either stick to reversibility and allow inner Subsets
- or allow z- and t- candidates.
The fact is, the second way is much more powerful.