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Advanced methods and approaches for solving Sudoku puzzles

Re: Braid Analysis

Postby SpAce » Mon Aug 20, 2018 5:02 pm

rjamil wrote:What I understand is that all pattern based techniques are non-assumptive as they never produce contradiction later.

Well, as I tried to explain in my response to Gordon, that definition is pretty hard to apply because there's no agreement on what constitutes a pattern in the first place, and even if there is, it has little to no connection to assumptiveness necessarily. Is a Discontinuous Nice Loop a pattern? Most people would say yes, I bet. Yet it starts with an assumption and produces a contradiction which proves the initial assumption false, so by that definition it's clearly an assumptive technique.

In fact, it's the only definition I think is pretty unambiguous: if a technique starts with an assumption and ends up with a contradiction (or that is the goal), then it's an assumptive technique. (It would be also if the initial assumption could be proved to be true, but I can't think of how that would work in this context.) In those cases the potential elimination/placement target is the initial assumption and nothing else, while truer patterns prove something about their environment instead of themselves.

By that definition things like Nishios, Discontinuous Nice Loops, APEs, JE incompatible-pair checks, etc are clearly assumptive techniques. On the other hand, a Kraken or an AIC-Net is not, even though Gordon among others claim they are (without any logical arguments demonstrating what is actually being assumed when using those techniques). To me it's pretty self-evident that there must be an assumption of some kind when something is called assumptive, and vice versa.

So I guess that all pattern based techniques contain non-assumptive property too; and rest, that can't be presented in pattern, contain assumptive property.

I don't think that's an accurate definition because of reasons mentioned above.

My question is that, is Braid analysis technique contain non-assumptive property?

With my limited understanding of Braid analysis, I wouldn't make any judgment call, but I don't think it's an intrinsic property of it one way or another. I'd guess it depends on how it's used in combination with other techniques.

Note: one more term that cause not only confusing but hurt sometime is degenerative.

True, I hadn't thought of that one :)
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Re: Braid Analysis

Postby StrmCkr » Mon Aug 20, 2018 5:07 pm


asides this is a thread of discussions on Braiding.... and shouldn't be hijacked for a different discussion.
Last edited by StrmCkr on Tue Aug 21, 2018 4:51 pm, edited 2 times in total.
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Re: Braid Analysis

Postby rjamil » Mon Aug 20, 2018 5:35 pm

Hi SpAce and StrmCkr,

Looking your explanation makes more confusion. (looks more off-topic)

What I think about assumptive techniques (for example, unique based constructs) is that they need to be backtrack when reached zero state (good definition and logic - zero state proposed by StrmCkr).

As far as one module cover all cases of "Transport" xy- xyz- wxyz-wings is concern, I define patterns instead of one module because its hit and miss chances are reduced result module become fast and efficient.

Now back to this thread topic: (but the above off-topic discussion help explaining what I asked is related to this thread)

I thought that Braid analysis is non-assumptive, i.e., it will never reached to zero state (irrespective of its multiple names and multiple people analyze. Thanks to DPB who summarized in this thread) but very complex algorithm to detect. I need more deciphering its pattern in order not to easily understand but write a module too. (Since, most of the eliminations that happened later are covered by this technique and those techniques become degenerative).

Otherwise, I will drop analyzing it for long time and will consider the same after all non-assumptive techniques analyzed and/or programmed.

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Re: Braid Analysis

Postby SpAce » Mon Aug 20, 2018 10:03 pm

rjamil wrote:Now back to this thread topic

That would be actually nice. I'd like to see a working example of a useful braid deduction that really helps in a tight spot (based on the comments I've gathered David's example doesn't work as is). I did some experimenting on my own last year but the only things I got out of it were trivially solvable otherwise, such as this:

http://forum.enjoysudoku.com/a-simple-braid-example-t34289.html

Soon after that I stopped bothering with this technique.
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Re: Braid Analysis

Postby SpAce » Mon Aug 20, 2018 10:13 pm

Sorry, this is again a bit off topic.

David P Bird wrote:(6a)r1c1 = (6-1)r3c2 = (1)r9c2 - (1=34)r78c1 - (4=8)r5c1 - (8)r5c8 = (8-5)r4c8 = (5b)r1c8 - (5=9c)r1c3
=> [ab]r1c1 <> 5, [ac]r1c1 <> 9

Interesting! I asked about the acceptability of multi-headed AICs (which I called AIC-Hydras) some time ago. Had I known that David himself uses them I wouldn't have needed to ask :)

At this point no further linear chains seem to be available (but I stand to be corrected).

Hodoku manages to squeeze a few more out of it before resorting to forcing chains:

(2)r2c7 = r6c7 - r5c9 = (2-7)r5c2 = r4c3 - (7=5|9)r4c7 - (5937=1)r7c8,r789c7 => -1 r2c7
(2)r5c9 = (2-7)r5c2 = (7-1)r9c2 = r3c2 - r9c3 = (1)r2c9 => -2 r2c9
(1)r2c9 = r3c9 - r3c2 = r9c1 - (1=34,8)r785c1 - (8=37,5)r571c8 => -5 r2c9
(7)r8c3 = r4c3 - (7=5|9)r4c7 - (5913=7)r789c7,r7c8 => -7 r8c9
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Re: Braid Analysis

Postby David P Bird » Mon Aug 20, 2018 11:17 pm

What do you want – another aunt Sally to throw yet more criticisms at? As you accept anything-goes methods, then you don't need Braid Analysis, and if I took the effort to find a good example, you would just shrug it off. Read the comments section in the opening post – I have made no exaggerated claims for the approach.

The three of you had no qualms in infuriating me by going way off-topic, so you should not expect me to waste time responding to your queries.

RJ Your first post only asked about similarities and carried an insinuation that my work was plagiarism. Your second post then made the comment that the opening post was later than the paper you cited – if you weren’t interested why make the comment? As it was, there was an insinuation that I was presenting 'alternative facts'. That was enough for me. I was (and still am) a scientist and believe in being honest in what I write.

I have reported your off-topic posts to Jason, and I hope that, this time, he will see things my way.

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Re: Braid Analysis

Postby blue » Tue Aug 21, 2018 12:26 am

(deleted)
Last edited by blue on Tue Aug 21, 2018 1:43 pm, edited 2 times in total.
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Re: Braid Analysis

Postby SpAce » Tue Aug 21, 2018 1:09 am

David P Bird wrote:What do you want – another aunt Sally to throw yet more criticisms at?

Are you talking to me? I must assume you are, though I thought you'd decided not to.

As you accept anything-goes methods,

True. I just used the full networking power of your other invention GEM to solve your example puzzle quite easily. It wasn't very satisfying that way, though, so it actually isn't how I'd like to solve puzzles if I had alternatives for tougher ones. But hey, not all of us are at your level, so we must work with what we have.

then you don't need Braid Analysis,

False. As I said in my own post about the topic, I find it interesting in principle and even adjusted my mark-up to support it. I've just lost interest after having neither found nor seen truly useful examples of it.

and if I took the effort to find a good example, you would just shrug it off.

Let's make a couple of things clear. First, I didn't ask YOU to take the effort to do anything. I fully expect you to ignore me. Secondly, you're making baseless assumptions again, which ticked me off in the first place. I would really like to see a good example of braiding by anyone, even though I don't expect to find many practical uses for it.

Read the comments section in the opening post – I have made no exaggerated claims for the approach.

Have I said or insinuated otherwise? (Somehow "exaggerated claims" rings a bell, though :) )

RJ Your first post only asked about similarities and carried an insinuation that my work was plagiarism. Your second post then made the comment that the opening post was later than the paper you cited – if you weren’t interested why make the comment? As it was, there was an insinuation that I was presenting 'alternative facts'. That was enough for me. I was (and still am) a scientist and believe in being honest in what I write.

And I fully understand you. If I feel my honesty is being questioned, it's one of the few things that really make me lose my cool. But you know that already. It's a bit ironic seeing you so sensitive about the same thing. ;)
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Re: Braid Analysis

Postby David P Bird » Tue Aug 21, 2018 11:41 am

Space in your line-by-line dissection of my post you have overlooked one of them:
The three of you had no qualms in infuriating me by going way off-topic, so you should not expect me to waste time responding to your queries.

As you should have discovered, undisciplined posting has made researching our past threads extremely hard work. This is something that I've tried to redress by writing some informative pieces, and I only wish that our mathematicians would do the same (Blue). Now in that light, perhaps you will appreciate that I don't welcome contributors who treat such threads as chat rooms. If you have another topic to raise, start a new thread. The 'He started it' excuse doesn't hold with me either, it just condones the previous writers behaviour and shows an equal lack of consideration.
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Re: Braid Analysis

Postby coloin » Wed Aug 22, 2018 12:28 pm

Indeed , its very easy to misinterpret comments.
Discussions on assumptive solving techniques has always been a topic which caused many arguments .... it was on the "eureka " forum and perhaps someone could dig it out and we can all chuckle.
For my part I struggle to solve any hard puzzle, I baulk at uniqueness solving methods and I still fail to see the difference between "logical guessing" amd chains AIC exocets nets etc etc
But each to his own ... and never was it more obvious when the first sudoku world championship was won by a women who guessed the last deciding puzzle !!! [ Thomas Snyder was not amused]

However for everyone's information ... the great "Dennis Berthier" has a solving technique which he calls "braids" which has nothing to do with the traveling numbers in the 3 minirows.

My main point however ...... and I hope David agrees ... is that the incidence of braid and non-braid [rope] minirows is significantly different , braid patterns being way more common ? x 20
So if you see a braid/rope dilemma in a puzzle .... however unpalatable it might seem, its significantly more likely to be a braid .... :roll:
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Re: Braid Analysis

Postby SpAce » Thu Aug 23, 2018 2:15 pm

coloin wrote:Discussions on assumptive solving techniques has always been a topic which caused many arguments .... it was on the "eureka " forum and perhaps someone could dig it out and we can all chuckle.

It would be fun to see. I'd really like to see counter-arguments to the points I've made about the mis-labeling of certain techniques as "assumptive" when there's no clear assumption around. To me it seems to be often used as a catch-all derogatory label for any technique someone doesn't deem worthy for any reasons. Anyway, this is my last comment about that in this thread, and sorry about that too.

My main point however ...... and I hope David agrees ... is that the incidence of braid and non-braid [rope] minirows is significantly different , braid patterns being way more common ? x 20
So if you see a braid/rope dilemma in a puzzle .... however unpalatable it might seem, its significantly more likely to be a braid .... :roll:

That's valuable information for someone using truly assumptive methods, as it would lead to better informed guesses (assuming a rope pattern should in most cases lead to a contradiction). Btw, has someone investigated how much the presence of a rope affects the difficulty of the puzzle? I would imagine that puzzles with rope patterns are generally easier, but is there any truth to that?
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Re: Braid Analysis

Postby SpAce » Thu Aug 23, 2018 3:18 pm

David P Bird wrote:As you should have discovered, undisciplined posting has made researching our past threads extremely hard work. This is something that I've tried to redress by writing some informative pieces, and I only wish that our mathematicians would do the same (Blue). Now in that light, perhaps you will appreciate that I don't welcome contributors who treat such threads as chat rooms.

Yes and no. I understand that it does increase chaos and makes finding the truly valuable pieces of information harder. However, free exchange of ideas has also the side-effect of creating those valuable pieces of information, while a tightly disciplined or even censored approach usually has the opposite effect. (Extreme examples of the latter can be seen in some feminist forums, where pretty much anything you say can be used against you and lead to a warning or getting kicked out. I once accidentally joined a misnamed feminist gaming group and can't think of a worse dystopia than their idea of "free" speech, which amounted to an echo chamber.)

That being said, I really appreciate the informative pieces you've written on various topics. From my point of view I'd like to propose one improvement to them, though. Even though a condensed format is good for a quick reference, it's not how I learn best. I like to read the background and the evolution of a technique if possible, which in many of these cases is buried in some old and long threads that can be numerous and hard to find (as you said). I think it would be great if your pieces included links to those background threads as well.
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Re: Chat Room

Postby David P Bird » Thu Aug 23, 2018 3:35 pm

Go to the house of Abdul the taxidermist.
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Re: Chat Room

Postby SpAce » Thu Aug 23, 2018 3:54 pm

David P Bird wrote:Go to the house of Abdul the taxidermist.

I think that would be easier for rjamil.
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Re: Chat Room

Postby SpAce » Thu Aug 23, 2018 9:42 pm

David P Bird wrote:This was previously an informative thread on Braid Analysis but it was very deliberately vandalised.

(Emphasis added). Keeping up the good work of assuming, I see, even though you say you don't like assumptive methods. Apparently being a master sudoku player comes with mind-reading powers, which definitely gives me more motivation to study harder! Then again, I haven't seen examples of very good mind-reading from you thus far, at least as far as my mind is concerned. I don't think any of us deliberately vandalized your work, but of course I can only speak for myself. From my point of view, what you say above is a totally baseless accusation.

I have therefore pulled the opening post and renamed the thread Chat Room. It was not such a good post anyway as the example it used was flawed.

That's one way to react. Instead of finding a better example or letting someone else do it, you threw out the good parts too. That I would call deliberate vandalism. Seems to me that if you don't hear 100% praise, you only hear 100% criticism. I for one have praised your efforts and creations in a lot of places, but I guess you're deaf to that, because it's not all I've said. I will also continue to say both things, despite your attitude, because I call the shots as I see them.

I hope that this will encourage Jason, whenever he returns, to take a firmer control of the loose cannons who post off topic throughout the forum.

You really want to turn this into one of those orwellian forums I mentioned above? One in which everyone has to be on their toes all the time so they wouldn't be reported to the authorities? Based on your repeated requests for such, I guess you would actually like that kind of an environment. Nothing wrong with that per se -- as far as I'm concerned, everyone is free to like what they like -- but I know I wouldn't. I do understand and support a certain level of discipline, but too much of it kills intellectual curiosity and creativity. Ironically it can also turn against those who wished it in the first place, which actually happened in that group I mentioned -- some people got quite surprised when they found out that the same rules applied to themselves as well.
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