The New Sudoku Players' Forum

[Pat]

Every puzzle that has exactly one solution is valid.

I agree, but the puzzles that have many solutions are valid too.

yes!

we like puzzles with exactly one answer,
but others are valid too

[eleven]

Guessing is not logic. It's random. Brute-force is guessing. Logic is based on reason not guessing.

From the very point, where you made your guess, you are using pure logic.
How do you decide, where you make the guess ? When your are looking for a skyscraper or swordfish, where do you start ? With number 1, or randomly ?
Most brute force solvers start with bivalue candidates scanning the cells top-down, left to right. This is a solid and pure logic plan.

You can like or dislike, what you want, but don't tell us, what logic is or not.

[yzfwsf]

Isn't the number of CSP-Variables in a braid the same as the number of strong inferences in the corresponding dynamic chain?
I'm not convinced that substituting 'dynamic chains' for 'braids' and 'strong inferences' for 'CSP-variables' would make the sentence false.

I think the length of the denis_berthier's chains is equivalent to the recursion depth of BFS.

[denis_berthier]

Isn't the number of CSP-Variables in a braid the same as the number of strong inferences in the corresponding dynamic chain?
I'm not convinced that substituting 'dynamic chains' for 'braids' and 'strong inferences' for 'CSP-variables' would make the sentence false.

The numbers are the same if there are no inner Subsets.
But SE doesn't count the number of "strong inferences"; it counts the total number of inferences (the "nodes"). That makes a huge difference. As I said, it allows to define braids of a fixed length as a pattern; it doesn't allow to define dynamic chain with a fixed number of nodes as a pattern.

[denis_berthier]

Isn't the number of CSP-Variables in a braid the same as the number of strong inferences in the corresponding dynamic chain?
I'm not convinced that substituting 'dynamic chains' for 'braids' and 'strong inferences' for 'CSP-variables' would make the sentence false.

I think the length of the denis_berthier's chains is equivalent to the recursion depth of BFS.

The maximum length, yes; obviously not the length of any individual chain.

[marek stefanik]

I think the length of the denis_berthier's chains is equivalent to the recursion depth of BFS.

But that's true for dynamic chains too, isn't it? That's what determines the SER.

Isn't the number of CSP-Variables in a braid the same as the number of strong inferences in the corresponding dynamic chain?
I'm not convinced that substituting 'dynamic chains' for 'braids' and 'strong inferences' for 'CSP-variables' would make the sentence false.

,
The numbers are the same if there are no inner Subsets.
But SE doesn't count the number of "strong inferences"; it counts the total number of inferences (the "nodes"). That makes a huge difference. As I said, it allows to define braids of a fixed length as a pattern; it doesn't allow to define dynamic chain with a fixed number of nodes as a pattern.

I see, so you were saying that braids[length] can be defined as a pattern, not braids in general.
That's interesting, because the logic is the same no matter what the length is, and even braids of a given length can look completely different in the actual grid, but I think this depends on the definition of the word 'pattern'.

[denis_berthier]

Isn't the number of CSP-Variables in a braid the same as the number of strong inferences in the corresponding dynamic chain?
I'm not convinced that substituting 'dynamic chains' for 'braids' and 'strong inferences' for 'CSP-variables' would make the sentence false.

,
The numbers are the same if there are no inner Subsets.
But SE doesn't count the number of "strong inferences"; it counts the total number of inferences (the "nodes"). That makes a huge difference. As I said, it allows to define braids of a fixed length as a pattern; it doesn't allow to define dynamic chain with a fixed number of nodes as a pattern.

I see, so you were saying that braids[length] can be defined as a pattern, not braids in general.
That's interesting, because the logic is the same no matter what the length is, and even braids of a given length can look completely different in the actual grid, but I think this depends on the definition of the word 'pattern'.

I define a resolution rule as a 1st order formula "pattern ==> elimination/assertion". In this view, a braid[n] can be defined as a pattern and it is precisely defined as such in my books (and directly implemented as such in CSP-Rules).
However, defining "braid" as a pattern would require an infinite disjunction on length, which is not 1st order. Of course, the braid[1], ... braid[n] form a family of similar (but logically not identical) patterns.

You may consider this as an irrelevant subtlety, but that's what allows the development of the whole theory (definition of all my ratings in pure logic terms, stability of the ratings under isomorphism, proof of T&E vs braids theorems, confluence of the T-braids theories, ....).
How a pattern visually looks on a grid is secondary (though of course important when it comes to spotting them); what counts is the underlying logic. In the case of chains, each building block (each link in the natural language sense) is similar to any other.

Now you may wonder why there is absolutely zero theory of dynamic chains or of any of the other chains that have appeared in the Sudoku literature. The reason is very simple: they can't be defined as patterns. Their various restrictions (leading to the different ratings) are based on the number of inference steps ("nodes"), which can't be expressed in any logical formula. The origin of all this is clear: it is the obsolete view of chains as chains of inferences and their lack of foundations in logic (I mean FOL).
(In the case of Robert's tracks, it's still worse: there's no notion of length in his original version - but it seems he has now adopted mine).

[Pupp]

I don't think using brute force makes it invalid. As long as there is only a single solution, then the puzzle is valid.

I can't really talk about nested dynamic chains, but if you're at the point where your solving puzzles harder than 9.5, your probable smart enough to figure out what exactly, a nested dynamic chain is.

That being said, at that point, I suspect the biggest problem a person has in solving a puzzle at that level is having enough of a memory to keep track of everything. From what I've heard, it can take hours to solve a puzzle that's over 11 SE.

I heard that X-Sudoku has problems over 12 SE.

[m_b_metcalf]

I heard that X-Sudoku has problems over 12 SE.

You'll find a list of Xtreme puzzles here.

Mike

[Pupp]

I don't think it's possible to make a unique solution puzzle that can only be solved with brute force.

Now, there are 2 types of solvers.

1. Solvers that use logic to solve every step to the end of the puzzle. It's the version that most programmers aspire to create.

2.Brute force solvers. They don't use logic to solve puzzles. They quickly guess the answer and cross check. There's only so many guesses needed to validate a puzzle. It's purpose is to just validate that a puzzle has only one solution. I'm guessing it's used mainly by programs churning out puzzles to toss puzzles with multiple solutions.

[Mathimagics]

All software solvers use logic.

I think by "logic" you actually mean something like "solving technique", eg Naked/Hidden sets, various varieties of fish, etc.

It's true that brute-force solvers are faster (and simpler), and that they are most commonly used for puzzle validation (uniqueness testing), and related tasks like finding minimal puzzles.

As with hardware, it's good to select the right tool for job! As a programmer, one simply aspires to produce the best software for that job.

[denis_berthier]

there are 2 types of solvers.
1. Solvers that use logic to solve every step to the end of the puzzle. It's the version that most programmers aspire to create.
2.Brute force solvers. They don't use logic to solve puzzles. They quickly guess the answer and cross check. There's only so many guesses needed to validate a puzzle. It's purpose is to just validate that a puzzle has only one solution. I'm guessing it's used mainly by programs churning out puzzles to toss puzzles with multiple solutions.

I wouldn't say it that way. There are indeed conceptually two types of solvers, corresponding to different and opposite goals (readability vs speed):
- pattern-based,
- based on structured search (DFS, BFS, T&E, ...); they are the fastest.

But, among the pattern-based solvers, there are two sub kinds:
- solvers based directly on pattern-matching: AFAIK, CSP-Rules is the only one of this kind (not counting the toy solver included in the CLIPS examples);
- solvers based on procedural code and in particular on some form of T&E, BFS or DFS for chains. It's hard to say that such solvers "use logic for every step" (unless you stretch the meaning of "logic" to "anything that isn't false").
.

[Serg]

Hi, Denis!

... among the pattern-based solvers, there are two sub kinds:
- solvers based directly on pattern-matching: AFAIK, CSP-Rules is the only one of this kind (not counting the toy solver included in the CLIPS examples);
- solvers based on procedural code and in particular on some form of T&E, BFS or DFS for chains. It's hard to say that such solvers "use logic for every step" (unless you stretch the meaning of "logic" to "anything that isn't false").

Do you really mean that your approach doesn't use any form of "T&E, BFS or DFS" for spotting whips/braids?

Serg

[denis_berthier]

Hi, Denis!

... among the pattern-based solvers, there are two sub kinds:
- solvers based directly on pattern-matching: AFAIK, CSP-Rules is the only one of this kind (not counting the toy solver included in the CLIPS examples);
- solvers based on procedural code and in particular on some form of T&E, BFS or DFS for chains. It's hard to say that such solvers "use logic for every step" (unless you stretch the meaning of "logic" to "anything that isn't false").

Do you really mean that your approach doesn't use any form of "T&E, BFS or DFS" for spotting whips/braids?

YES. It is pure pattern-matching.

[Serg]

Hi, Denis!
Could you post an example of spotting some whip/braid? I'd like to see not final result (which can be found in "Puzzles" division of this Forum), but steps of finding some whip/braid. It looks like you know magic way of intellectual search of a pattern w/o some BFS, DFS etc.

Serg