The New Sudoku Players' Forum

[eleven]

The example notation you provided does not translate into a straightforward and ordered set of logical statements that prove the elimination.

??

Eleven, by refusing to even try to work out what I am saying in my third point you are making this exchange between us far more painful than it need be. Previously I even gave you an example of a notated chain segment translated into English to help you which I wonder if you even looked at.

Your English is very good, so please tell me what part of my sentence you don't understand and I will reword it if necessary.

When we have worked this through I hope that you will see that your example notation does not qualify as being a stream but is more a whirlpool of different facts.

I read it again, but still don't know what you mean at all. I looked back to the other post, i didn't understand:

[Taking your suggested implication stream
UR 45r79c48: 9r9c3 or 3r7c8 (at least one must be true)
3r7c8 (-> r7c7=45) -> triple 456r147c7 (-> r2c7=17) -> triple 137r2c279 (-> r2c4=4) -> pair 45r27c3 -> r9c3=9
=> r9c3=9 (in both cases)
I find you leave a lot of gaps for the reader to bridge, eg r9c3 & r9c8 don't appear anywhere in the main stream.

Applying a disciplined approach there are no gaps
(9=45)r79c3 -UR- (45=3)r79c8 - (3=456)r147c7 - (46#1=17#1)r2c7 - (137=4)r2c239 - (45=9)r79c3 => r9c3 = 9
...

Can you see it now ?

UR 45r79c48: 9r9c3 or 3r7c8 (at least one must be true)
3r7c8 (-> r7c7=45) -> triple 456r147c7 (-> r2c7=17) -> triple 137r2c279 (-> r2c4=4) -> pair 45r27c3 -> r9c3=9
=> r9c3=9 (in both cases)

Or is it that there are 2 lines (for the 2 possibilities) ? Why should i press it into one line, if it's that easier to read in two ?

[blue]

The pattern based strong-only link I was trying to remember is between two possible disrupting candidates for a deadly pattern that would result in a contradiction (or – under my breath - two possible solutions).David

An example that doesn't involve contradicting a uniqueness assumption, is disruptors for "oddagon" patterns.
There you have that at least one of the disruptors must be true (in a solution) -- an OR relationship.
In the general case, two or more of them being true is not impossible ... making it an ordinary/non-exclusive OR relationship.

Fortunately, XOR or OR, it doesn't matter (for oddagons or otherwise) ... (A XOR B) is ((A OR B) AND NOT(A AND B)), and the only (A OR B) part is required to complete the usual chaining arguments.
On the technical side, there's also this: Any difference between using XOR -vs- OR, for a strong link (strong-congugate -vs- strong-only) ... vanishes ... as soon as you 1) chain it with a weak/NAND link and, 2) supress any detail about possible truth values for the linking candidate/node and focus only on the logical relationship between the possible truth values for the endpoint nodes.
I'ld show some truth table data, but it would be technical (and possibly pointless), and I'ld hate to see it causing a diversion from the rest of the conversation (such as it is).

[DonM]

DonM,

Readers here, including me, would better understand your reason for conflating the subjects of manual solving and notation if you provided an example or two where, as you say, the Eureka notation provides an advantage. The complexity of the examples should be consistent with the solutions being posted here, by near-beginners in some cases.

Thanks for the homework professor, but I have already spent considerable time explaining the important relationship between manual solving and notation and how they are in many ways integral (perhaps a subset of conflation). Given the history over years of the relationship of manual solving and notation with enough evidence still present on the internet to explain it, any interested reader can find it without examples from me.

Besides, the close relationship between manual solving and the notation and how one benefits the other is as far as I'm concerned self-evident to you or 'readers here'. My guess is that you're more interested in having something to critique for purposes of your own self-interest. Here's some homework for you: Why not offer a constructive position in this discussion rather than the contribution being restricted to posts meant to clarify whether you've been insulted or accused of supporting 'aHP' or 'HP'.

All that said, I actually have provided an example where the Eureka notation provides an advantage in posting my solution (yet to be corrected) to Gurth's puzzle. I was attempting to point out that even more difficult puzzles can be solved using relatively simple chains. The Eureka notation allowed those chains to be easily explained such that even newer solvers should be able to follow the solution and perhaps realize that they may be more able to solve difficult puzzles manually than they may have thought. That's how I learned. And that's my contribution however limited.

Language or a notation transmits an idea allowing the reader to not only understand the idea, but perhaps come up with their own new ideas and likewise transmit them. That's what happened through the years with manual solving and the Eureka notation by Myth Jellies, SteveK, ttt and all those who took part in solving the UK Extremes or the 'Unsolvables'. Was nobody here paying attention?

[eleven]

Besides, the close relationship between manual solving and the notation and how one benefits the other is as far as I'm concerned self-evident to you or 'readers here'

Here i have a completeley other point of view. A manual solver solves and does not think in notation. Only at the end there is the question, how she should notate this.
And - from manual solver to manual solver - in best case the notation also should reflect, how he found this.
I always liked to read Marty's solutions (on DailySudoko), until he tried to write them as AIC's. Same for Bat's (though he keeps to be original with using AIC).
I liked many of SteveG48's solutions, but they read like a computer dump.
From Steve K's blog i liked to read where/what he is looking at/for, and then i had to translate the notation for me ...
So, if people really like manual solving, they should use a free notation, one they think could help others best to see, how they found it.

[David P Bird]

DonM I'm very disappointed that you used a post addressed to me to continue your vendetta against Denis. DB and I know that we are in opposite camps but nevertheless are able to engage in blunt but civil exchanges albeit never agreeing much about anything but just sometimes one of us can benefit from the other.

Although there has been much truth in your posts you have gone in with both guns blazing which is almost guaranteed to ensure that arguments will get personal and no resolution will be reached. That's why now with my hair now grey I try to avoid that.

I have to accept that my comments aren't generally well received (quite the opposite usually) but I make them without malice hoping to provide brain food for people who I think are taking a blinkered view or are set to head in the wrong direction. When it's clear that they are unwelcome I hold off which is why I stopped contributing much to this puzzles section.

In this discussion I waited for temperatures to cool before trying to bring the focus back on the key issues, but I'm probably the least appropriate person to try to lead any movement to change things. The cool reception my Junior Exocet Compendium got proved that beyond doubt. It was my 2nd attempt to provide a single reference source on the subject which I considered was sorely needed.

DPB

[David P Bird]

Eleven please see the last but one paragraph in my post < in my post of Aug 9th> giving you the link I mentioned.
There you will see that I was able to put each link into words (reading backwards, but that's not so important) over a section of the chain taking them in exactly the same order.

I would like to see how you do the same for your 'intuitive chain' as it would help me understand your conventions.

While your complaint that there is no up to date reference on how to notate the Booleans in Eureka AICs is justified, why is it that there is no equivalent reference for your notation style?

David (in haste)

[DonM]

DonM I'm very disappointed that you used a post addressed to me to continue your vendetta against Denis. DB and I know that we are in opposite camps but nevertheless are able to engage in blunt but civil exchanges albeit never agreeing much about anything but just sometimes one of us can benefit from the other.

Although there has been much truth in your posts you have gone in with both guns blazing which is almost guaranteed to ensure that arguments will get personal and no resolution will be reached. That's why now with my hair now grey I try to avoid that...
DPB

I'm sorry you feel that way. My posts have been civil and there has been no name-calling which is usually the mark of posts that have become personal. But, if I'm not mistaken, you've fired some shots as well when you've felt misrepresented in one way or another. Anyway, no one posting here has ever come across as a babe in arms or paragon of diplomatic virtue.

For my part, I don''t dance around the bush and avoid confronting what the real issues are when individuals with agendas are running a topic off the rails (fwiw: I'm not including you). And regarding civility, I have complimented you, eleven and ronk and on two occasions I offered apologies where necessary. We see what we want to see.

This discussion has become like the Mad-Hatter's Tea Party. Doesn't it have to do with the fact that an otherwise proven notation is being used in a way that was never intended by, presumably, manual solvers? If the topic isn't closely connected with manual solving, then is the subject that a notation used by a computer solver is the solution because it really doesn't matter whether the puzzle is solved by human or computer?

And, in the end, what is the purpose of all the discussion of AND, OR, XOR etc.? I know what Boolean operators are. I have been a computer programmer: I wrote one of the first major commercial 'microcomputer' Financial Management packages for physicians back in the 1980s using both the original C and Basic Compiler. Let's make this simple: 90% of the alleged limitations of the Eureka notation as used on this forum could be solved by the simple expression of nets using the old-fashioned vertical format.

[JasonLion]

I suspect that it all comes down to a lack of a agreement on what the criteria should be for choosing one system of notation over another. Someone proposes a system of notation, or more likely a variation on some existing notation, and while there seems to be no shortage of opinions, we have no real basis for reaching a consensus on using it or not.

People have suggested some elements of a criteria for judging notation: easy to read, east to write, easy to learn, containing a logical proof of the step notated, brief, well documented, elegant, suitable for manual solvers, suitable for machine solvers, and so on. But we don't seem to agree on how to judge the individual elements, let alone prioritize them relative to each other and resolve their mutual contradictions.

Without some progress on criteria for preferring one notation over another, we just continue to go around in circles, repeating old old arguments again and again.

Having a uniform, agreed upon, notation would certainly help some things. But this particular conversation doesn't seem to have moved us any closer to that (at least so far).

[denis_berthier]

I've always considered that theoretically it's possible to start chains from an OR inference where both arguments could be true. These have been called strong-only links because it's impossible for both terms to be false. For example if two cells contain three candidate digits there is a strong-only link between two of them as they would both be true if the third one is false.

I can't see your point. For the two cells, say (r, c) and (r, c'), you have XOR(n1rc, n2rc, n3rc) XOR(n1rc', n2rc', n3rc'). I don't see how you turn this into a chain.
In any case, the fact that all the chains are XOR/NAND is the fundamental of AICs, or it should be if AIC is intended to mean anything.

An AIC alternates between strong and weak links.[...]Thus an AIC is an OR/NAND chain.
In practice, most strong links are also weak, and thus correspond to XOR. However this is not always true, and is not required for the logic of an AIC to work.

Until now, I haven't seen any convincing example.
If an OR link is not XOR, it means the two candidates it relates are related only by indirect OR. Which is very likely to mean that the pattern is not fully or not correctly defined.
As an outsider wrt to AIC notation, but considering the type of chains it was designed to notate, I have very strong doubts the original AIC notation was intended to allow such indirect OR links.

[daj95376]

[Withdrawn:]

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[denis_berthier]

Code: Select all

                 (1=5)r4c4 -
                /           \
 ... (6=1)r3c4 -              (5?6=3)r6c5 ...
                \           /
                 (1=6)r2c5 -


I'm pretty sure that "?" means OR when read l-to-r, but it also means XOR when read r-to-l.

How could 2 digits in the same cell (r6c5) be related by OR but not XOR?

[denis_berthier]

XOR or OR, it doesn't matter (for oddagons or otherwise) ... (A XOR B) is ((A OR B) AND NOT(A AND B)), and the only (A OR B) part is required to complete the usual chaining arguments.

It matters for the manual solver or the software in terms of complexity.
As in any case you have to look for the NAND steps, knowing in advance that the OR steps are in fact XOR ones, i.e. they are among the NAND ones, will simplify the search for them.
To take an obvious example, no one would look for conjugate pairs for two cells that are not in the same row/col/block.

[daj95376]

[Withdrawn:]

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[denis_berthier]

daj95376,
I didn't say the XOR was necessary to prove the l-to-r inferences.

You don't answer my simple question:
How could 2 digits in the same cell (r6c5) be related by OR but not XOR?

[daj95376]

[Withdrawn:]

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