The New Sudoku Players' Forum

[denis_berthier]

I would definitely favor a convention of listing the t-candidates first and then the z-candidates to put both closer to their linked partners.

I didn't mean to be so precise, but ok. And then you can also add that the t-candidates are listed in the order from closest rlc to farthest rlc.

the z-candidates are extra right-linking-candidates

I wouldn't say this. Both z- and t- candidates could be used as alternative left-linking-candidates in a braid.

[SpAce]

I would definitely favor a convention of listing the t-candidates first and then the z-candidates to put both closer to their linked partners.

I didn't mean to be so precise, but ok. And then you can also add that the t-candidates are listed in the order from closest rlc to farthest rlc.

Good point! I definitely concur with that further adjustment. All of that makes it easier for the reader to see the remote links.

the z-candidates are extra right-linking-candidates

I wouldn't say this. Both z- and t- candidates could be used as alternative left-linking-candidates in a braid.

You're right. If the chain is started with the target then both t- and z-candidates are "extra llcs". That's the simpler point of view because it doesn't need any form of OR-branching (in the left-to-right direction). However, it's the one that requires fixing the target when building the chain.

What I said in the above quote is true only when the chain is built/seen as a non-contradiction chain. In that pov the z-candidates are alternate end-points ("final rlcs") ORed with the non-final rlc.

(Even such minimal OR-branching is an obvious complication, which makes it difficult to build z-chains (and zt-whips) without a fixed target. That's why I think z-chains are actually more complex than t-whips. The opposite is true only if both are seen as contradiction chains and started with the target.)

[denis_berthier]

... which makes it difficult to build z-chains (and zt-whips) without a fixed target. That's why I think z-chains are actually more complex than t-whips. The opposite is true only if both are seen as contradiction chains and started with the target.)

I don't see it this way. Take their relative complexity wrt to a bivalue-chain: in a t-whip, you may have additional candidates linked to any rlc; in a z-chain, additional candidates can only be linked to one candidate, the target. The complexity of t-whips increases faster than that of z-chains.

[SpAce]

... which makes it difficult to build z-chains (and zt-whips) without a fixed target. That's why I think z-chains are actually more complex than t-whips. The opposite is true only if both are seen as contradiction chains and started with the target.)

I don't see it this way. Take their relative complexity wrt to a bivalue-chain: in a t-whip, you may have additional candidates linked to any rlc; in a z-chain, additional candidates can only be linked to one candidate, the target. The complexity of t-whips increases faster than that of z-chains.

It depends on the type of complexity we're talking about. You've said yourself that OR-branching is more complex than AND-branching, and with a z-pattern it's unavoidable either way the chain is traversed (i.e. it's a case of mixed branching in your terms) -- unless the chain is started with the target and ended with a contradiction.

Granted, it's very simple OR-branching, but it still has clear consequences for a manual solver, which is evident in the relatively complex algorithm I presented here. Can you suggest a simpler algorithm to avoid starting with a target?

This is very much related to what Robert has been asking of you: how do you find your patterns (z-chains and zt-whips specifically) without trying a specific target? With biv-chains, t-whips/braids, and forcing t-whips/braids it's easy. Both Robert and I can find them trivially using our slightly different manual methods, even if the resulting chain/net is long and complex, but that's not the case with z-patterns even if they're relatively short. As far as I see, the only way to find them easily is by starting with a target. If you disagree, please show us exactly how you think it can be done.

[denis_berthier]

Hi SpAce,

There's ZERO OR-branching in whips or braids.
The only pseudo OR-branching in my chains is g-candidates at right-linking places in g-whips and g-braids. This OR-branching is so tamed that it allows much fewer further left-linking candidates than an ordinary rlc.
If you don't agree with this, you have to exhibit OR-branching in my definitions, not in your imagination, where definitions and ways of finding patterns are alll mingled.

OR-branching is equivalent to reasoning by cases in maths, a technique logically valid, but that has always been considered as very inelegant. If this is what you want, use conjugated tracks with as many levels of T&E as you want or use Sudoku Explainer. SudoRules is not the good place for enjoying this kind of techniques.

[SpAce]

There's ZERO OR-branching in whips or braids.

True -- as long as they're used as contradiction chains/nets. That's how I originally thought you viewed and found them, so there was no question about it.

If you don't agree with this, you have to exhibit OR-branching in my definitions, not in your imagination, where definitions and ways of finding patterns are alll mingled.

Oh, I totally agree that your definitions don't have OR-branching. That just happens to be totally irrelevant to the current discussion which has been about finding those patterns all along. Nothing is mingled in my mind, thank you very much.

This discussion started when you said that you actually find your chains without locking a target, which surprised both myself and Robert. It naturally led to the question how you do it, by both of us, because it's far from obvious in the case of z-patterns.

You have now repeatedly failed to answer that question. Yes, we know that you start with partial whips, but that's as far as you've explained. So, once more:

If you disagree, please show us exactly how you think it can be done.

[denis_berthier]

There's ZERO OR-branching in whips or braids.

True -- as long as they're used as contradiction chains/nets. That's how I originally thought you viewed and found them, so there was no question about it.

"viewed and found " on the same footing: once more, confusion about defining a pattern and the ways of finding it.

If you don't agree with this, you have to exhibit OR-branching in my definitions, not in your imagination, where definitions and ways of finding patterns are alll mingled.

Oh, I totally agree that your definitions don't have OR-branching. That just happens to be totally irrelevant to the current discussion which has been about finding those patterns all along.

Wrong. The current discussion was about the relative complexities of z-chains and t-whips (of same lengths).

[SpAce]

"viewed and found " on the same footing: once more, confusion about defining a pattern and the ways of finding it.

<sigh> Sorry if I ignore your gaslighting.

Wrong. The current discussion was about the relative complexities of z-chains and t-whips (of same lengths).

No. The current discussion has been about the relative complexity of finding those chains. I've made it very clear, and I know you can read. You're just deflecting for some unknown reason. No one is trying to embarrass you in any way. I just want to know how you find z-chains and zt-whips, that's all. I guess the answer could be found in your code, but I'm not that interested. I don't know why you have such a hard time answering a simple question.

[denis_berthier]

I will not answer questions that I've already answered.

[SpAce]

I will not answer questions that I've already answered.

Yet more gaslighting. Sorry, but you can't make me question my sanity that easily. I believe my own eyes, and fact is that I haven't seen your answer anywhere. Apparently neither has Robert, because he also tried to ask (practically) the same question many times.

If you have explained it in some other thread or in your public book, please provide a link or a page reference. You can't expect us to have read everything you've ever published.

The closest explanation I remember seeing is this and what you have in the BUM (btw, I like the graphics), but both are very vague and hardly specific to z-patterns. What both I and Robert have been asking is some (or even one) real-world examples of the full process.