The New Sudoku Players' Forum

[DonM]

The problem with the wrong link is, that there is no ALS, because there are 4 candidates in 2 cells.

The ALS chains of Dan and Leren are out of question.

Personally i prefer, when such chains are written as simple as possible, without pressing simple links into one ALS link.

E.g Dan's cahin i would write as
(46=7)r23c4-(7=1)r1c4-(1=8)r1c6-(8=146)r78c6,r7c5 => -46r8c4
and Leren's as
(467=8)r8c269-(8=1)r1c6-(1=7)r1c4-(7=46)r23c4 => -46r8c4

But i see, that you like to play with that to notate shorter solutions.

@Danny: if you have an ALS, you always have a link between different sets of candidates, e.g. abc=defg for a 6 cell ALS. The question is just, if it is of use It seems to be convention here to leave out candidates on one side, if they are not used (so a=b also would be a valid link in the 6 cell ALS).

In keeping with the subject of the posts above, beginning with David's, I believe that the use of the 'simplified' ALS notation mentioned by Eleven just above and other variations of notation that have been introduced are also contributing to the problem. For instance, to me, leaving out the 'unused candidates' of a 6-element ALS so that all that is notated is a=b results in an ALS notation that is both misleading and inaccurate. It is the entire pattern and thus, all candidates of an ALS that allows a=b so all candidates that make up an ALS need to be stated. This premise applies to all other patterns as well.

The basic Eureka notation became standardized after a lot of input (over 2 years or more) from people with a lot of math logic experience, but what we have here are changes being made to the notation by people who are relatively new solvers. There seems to be no rhyme or reason for it other than to reduce the notation to a form of shorthand that requires less typing at the price of accuracy and clarity for the reader.

PS. Just so it's clear, I realize that Eleven was simply stating what has been occurring by others rather than his promoting this 'simplified' notation.

[eleven]

I am neither promoting it, nor i find it bad.
If you are used to it, it is easy to understand. The cells tell you, what candidates can be in them. If there are n+1 candidates (n is the number of cells), it is an ALS and every link with different candidates is valid.
If you list all candidates you have the problem, that you would have to list say 3 candidates, but for the next weak link you only use one of them. This is confusing for the reader too.

[SteveG48]

The basic Eureka notation became standardized after a lot of input (over 2 years or more) from people with a lot of math logic experience, but what we have here are changes being made to the notation by people who are relatively new solvers. There seems to be no rhyme or reason for it other than to reduce the notation to a form of shorthand that requires less typing at the price of accuracy and clarity for the reader.

PS. Just so it's clear, I realize that Eleven was simply stating what has been occurring by others rather than his promoting this 'simplified' notation.

I'm obviously in the category of "relatively new solver", having never forged a Sudoku chain nor seen Eureka notation prior to coming here a bit over a year ago. What I do now is strictly what I've learned by following the examples that I've seen on the forum and through much appreciated direct instruction from several of the more experienced members. I'm also one the ones using simplified notation, but that's only because I've seen it done by others and it seemed to be accepted. (I also agree with Eleven that it can actually add clarity by not dragging in unused candidates.)

At this point I'd be interested in seeing a consensus from the group on what is and isn't appropriate. Should we use simplified notation or not? What are the feelings on this?

[DonM]

I am neither promoting it, nor i find it bad.
If you are used to it, it is easy to understand. The cells tell you, what candidates can be in them. If there are n+1 candidates (n is the number of cells), it is an ALS and every link with different candidates is valid.
If you list all candidates you have the problem, that you would have to list say 3 candidates, but for the next weak link you only use one of them. This is confusing for the reader too.

How can it be confusing to list all candidates that are part of a pattern when one is using the pattern to justify an elimination? Besides, that would infer that, all these years, the Eureka notation has been confusing when it comes to expressing basic pattern (such as ALS) eliminations. The weak link that is being expressed following an ALS is only possible because of the entire pattern of candidates. Leaving out the other candidates of the pattern forces the reader to figure out what the pattern is in the first place.

[JasonLion]

In my view the notation should be a proof. Some of the notational shorthand I have seen recently, while occasionally quite entertaining, fails to prove the solution and worse can sometimes leave even an experienced reader guessing at what was actually intended.

[eleven]

DonM,
Please look at this example from the other thread. How would you formulate it ?

[DonM]

The basic Eureka notation became standardized after a lot of input (over 2 years or more) from people with a lot of math logic experience, but what we have here are changes being made to the notation by people who are relatively new solvers. There seems to be no rhyme or reason for it other than to reduce the notation to a form of shorthand that requires less typing at the price of accuracy and clarity for the reader.

PS. Just so it's clear, I realize that Eleven was simply stating what has been occurring by others rather than his promoting this 'simplified' notation.

I'm obviously in the category of "relatively new solver", having never forged a Sudoku chain nor seen Eureka notation prior to coming here a bit over a year ago. What I do now is strictly what I've learned by following the examples that I've seen on the forum and through much appreciated direct instruction from several of the more experienced members. I'm also one the ones using simplified notation, but that's only because I've seen it done by others and it seemed to be accepted. (I also agree with Eleven that it can actually add clarity by not dragging in unused candidates.)

At this point I'd be interested in seeing a consensus from the group on what is and isn't appropriate. Should we use simplified notation or not? What are the feelings on this?

I wish there were enough truly experienced members here with an appreciation for the Eureka notation to give a valid consensus. IMO, the consistent motive behind the notation changes I've been seeing are mainly self-serving (ie. require as little typing as possible or using one's own notation because one thinks it's better) rather than for the benefit of the reader.

And while I'm on a roll, I can't help but think that the lackadaisical approach to notation has some connection with the fact that at least half of solutions here are coming from the uncredited use of computer solvers (self-programmed or otherwise). It is impossible to come up with a manual solution, notate it and type it into the forum within a very few minutes of a puzzle being posted, but that's what's going on. (Steve, to your credit, you aren't among the latter.)

[eleven]

I wish there were enough truly experienced members here with an appreciation for the Eureka notation to give a valid consensus.

Times are changing. Even the Eureka notation can be improved (or did you figure out a better classical notation for Steve's move ?)
Concerning the manual solving: Manual solutions are almost never optimal, there are many ways to skin a cat, should we stay sitting before the solved puzzle and ponder, if there could be a better one ?
If i have the time, i solve it and then look, how easier it could have been, if i have little time, i look how it can be solved, thats how i see it.

[gurth]

The discussion has gone off on a tangent about ALS notation, leaving my basic question unanswered.
Maybe I should explain why I say eleven's interpretation would be disastrous:
If (46= is to mean "if any part/s of 46 is/are missing" then there are too many possibilities to be practically helpful. If however it is to mean "if all 4s and 6s are missing" than we have only one possibility on each side of the '=' (OR) sign, which after all is the whole idea of using the OR concept: to separate the alternatives into two clear and single possibilities. To separate the alternatives into two complex sets of possibilities, as eleven wishes to do, is most undesirable and WILL be confusing. And also, of no practical use in most cases.

[DonM]

I wish there were enough truly experienced members here with an appreciation for the Eureka notation to give a valid consensus.

Times are changing. Even the Eureka notation can be improved (or did you figure out a better classical notation for Steve's move ?)

I've been through this with you before. Instead of addressing the point I am making, you change the subject with a fool's errand. The unwarranted oversimplification and changing of the Eureka notation going on here is not because solvers are regularly coming up with solutions that can't be notated any other way.

And times are not changing on this forum. All the puzzles are, by any standard, easy puzzles. One line solutions for ER=7.2 or less puzzles over and over do not promote innovation and growth in the solving experience. If these were ER=8.3 puzzles or greater, then it's conceivable that there might be solutions that required tweaking of the Eureka notation in order to express them correctly.

Concerning the manual solving: Manual solutions are almost never optimal, there are many ways to skin a cat, should we stay sitting before the solved puzzle and ponder, if there could be a better one ? If i have the time, i solve it and then look, how easier it could have been, if i have little time, i look how it can be solved, thats how i see it.

So are you saying that it is the solution that counts, whether computer-assisted or not? If one has the time, then go for a manual solution, but if one doesn't have the time, then go for the computer solver? Is that what sudoku solving has come to?

Still, I actually do understand the interest in programmers in comparing the solutions of puzzles using their various computer solvers. And sudoku solver programmers are pretty smart people. What I find very sad is the reality of a dying art as those using computer solvers mix in with, and become the majority over, those solving manually. And I don't understand the practice of individuals presenting solutions as their own (which infers no computer assistance) without crediting the use of a computer solver. It is disengenuous at the very least and is insulting to those who spent a lot more time coming up with a truly manual solution.

[David P Bird]

The discussion has gone off on a tangent about ALS notation, leaving my basic question unanswered.
Maybe I should explain why I say eleven's interpretation would be disastrous:
If (46= is to mean "if any part/s of 46 is/are missing" then there are too many possibilities to be practically helpful. If however it is to mean "if all 4s and 6s are missing" than we have only one possibility on each side of the '=' (OR) sign, which after all is the whole idea of using the OR concept: to separate the alternatives into two clear and single possibilities. To separate the alternatives into two complex sets of possibilities, as eleven wishes to do, is most undesirable and WILL be confusing. And also, of no practical use in most cases.

Gurth, I think some things slipped your mind while you took your extended leave. For a refresher on AICs see <here>

The terms are Boolean entities that must be only capable of being true or false
The operators such as "=" are separate from the terms and express the logical relationship between them. They don’t qualify the term preceding them as your writing suggests. That’s why I advocate using the #N qualifier when it's needed.

If we were to follow your suggestion then in the expression (ab)cells12 = (cd)cells12, "(ab)" would signify they hold exactly (a) and (b) and "(cd)" would signify they hold one or both of (c) and (d). There would then be two different meanings for equivalent terms.

[David P Bird]

Don good luck with your campaign, but I feel you are probably fighting a lost cause and the best that can be achieved is a bit of damage limitation. Your points are sound and well made but here's a couple more.

1) When mastering how to notate our logic properly it is much easier to error check ones work and see if everything is in order if they are kept verbose. For instance the realisation that 5 candidates in 3 cells are not an Almost Naked Set
2) Typing errors are common and can lead the reader on a merry dance when they happen, but are much easier to detect when there is a certain amount of redundancy in the notation. This then helps distinguish a slip of the finger from a flaw in the logic.

We are now in the age of the sound-bite and instant text exchanges with a general reluctance to add a single character more than absolutely necessary, but you only have to look at the time wasted on fruitless arguments in this section of the forum to realise this can be a false economy when logical paths have to be clearly conveyed.

[gurth]

If we were to follow your suggestion then in the expression (ab)cells12 = (cd)cells12, "(ab)" would signify they hold exactly (a) and (b) and "(cd)" would signify they hold one or both of (c) and (d). There would then be two different meanings for equivalent terms.

David, it seems to me you do not grasp what I am trying to say, but I'll try again...
I am now trying to use plain English to get across what I want the expression (ab)cells12 = (cd)cells12 to signify:
Firstly, it means "If not (ab)cells12, then (cd)cells12". (this is purely what the logical operator '=' means). So far, this agrees with ALL current interpretations. The problem is simply to define exactly what we mean by "if not (ab) cells12", and THIS is the crucial point in which I differ from eleven.
I say it should mean "if we remove all values (a) and (b) from cells12, then we can deduce (and context and other cells can play a part in this deduction), that cells12 must contain (c) and (d). "

The sign '=' does not mean, as you seem to think, equivalence or equality. There is no 'equivalence' in this expression.

I am about to give up on all posters here as hopelessly at sea about logic.

[daj95376]

Code: Select all

 +--------------------------------------------------------------+
 |  5     3     4     |  17    9     18    |  6     78    2     |
 |  67    679   8     |  467   2     5     |  3     49    1     |
 |  1     679   2     |  467   468   3     |  789   5     47    |
 |--------------------+--------------------+--------------------|
 |  36    145   7     |  8     1346  9     |  2     13    56    |
 |  2     14    36    |  1346  5     146   |  78    78    9     |
 |  8     15    9     |  2     136   7     |  4     13    56    |
 |--------------------+--------------------+--------------------|
 |  367   2     36    |  5     146   146   |  79    49    8     |
 |  9     67    5     |  346   3468  468   |  1     2     47    |
 |  4     8     1     |  9     7     2     |  5     6     3     |
 +--------------------------------------------------------------+
 # 58 eliminations remain


Gurth,

Outside of SK-Loops and V-Loops, I'm unaware of the notation ( wx = yz )cells ever being used. I've been arguing that it should be acceptable (as a representation of an AALS). A more accurate representation might be: ( w & x = y & z )cells. However, numerous people have rejected the first notation, and I doubt if they'd accept the second notation, either.

Now, to try and present the current perspective of -(yz)cells. Consider the original puzzle (above):

If r8c4=4 is true, then (-4=67)r23c4 follows. Three candidates are reduced to two candidates in r23c4. Similarly for r8c4=6 forcing (-6=47)r23c4. Any candidate, that prevents the pair 46 from forming in r23c4, automatically forces 7 to be true in one of the cells. Thus, the notation (46=7)r23c4. This is an ALS relationship.

Note: if (46=7)r23c4 implied that all candidates for 4 and 6 are removed, then we would have a contradiction where 7 must be true in both cells.

However, we have a different situation with (-4=368)r8c56 and (-6=348)r8c56. Here, four candidates are reduced to three candidates, but we can no longer conclude that any specific value is always true. I simply confused things by suggesting that (46=38)r8c56 existed. Sorry!!!

_

[David P Bird]

Gurth, I apologise for my misinterpretation of your post.

The following has been difficult to write and may seem insulting to you but that has not been my intention. Somewhere in this walk through is a point of misunderstanding between us and I believe this is the best way to reveal it.
--------------
In AIC logic
a weak link "-" is a logical NAND (NOT AND) operator indicating that both terms can't both be true (they could both be false).
a strong link "=" is a logical OR operator that indicates that the terms can't both be false (they could both be true).

Some players find it easier to express them this way:
For a weak link at least one of the arguments is false and possibly both are.
For a strong link at least one of the arguments is true and possibly both are.

These meanings are required to prove the deductions that Alternating Inference Chains provide, principally that two terms at the end of a AIC connected to it by strong links can't both be false.
A feature of AICs is that they are bidirectional and can be followed reading left to right or right to left.

Conjugate terms are linked by a logical XOR (exclusive OR) operator when one must be true and the other false. Conjugate terms are both weakly and strongly linked but must be used only in one of these ways within AICs.

Players who use forcing chains will find that for most of their lengths they are actually using alternating inferences but at some point the discipline of keeping the inferences alternating will be broken. For this reason it is useful for them to use the same weak and strong link symbols.
-------------

Now, for two cells holding (abcd) between them (ab#2) and (cd#2) are just two possible combinations out of the six available.
In AIC terms they are weakly linked as they both can't be true and could both be false when (ab) and (cd) each contain one true candidate.

Let's take this AIC chain
(a) = (b) – (c) = (d)
If (a) is assumed true (b) could be true or false so we get nowhere
Assuming (a) is false (b) is forced true, (c) forced false, and (d) true
Likewise if (d) is assumed false, reading in the reverse direction (a) must be true which proves the usual elimination rule.

Effectively by changing you interpretation of the notation, you are now trying to substitute a strong link with a weak one. But that logic is invalid, sure it will work sometimes but it won't work in every circumstance.