The New Sudoku Players' Forum

[denis_berthier]

I think, there is nothing magic with this method.

That was just a way of speaking. The "magic" is, the complexity of the puzzle is reduced (whatever measure of complexity you take: W, SER, ...). And this has to be explained.

If you mean the complexity of finding the other puzzle, it's like with the other techniques - sometimes easy, sometimes hard, independent of, if it leads to nothing or solves the puzzle directly.

Not exactly. The complexity of a NQ is well defined a priori (whether it leads to any elimination or not and whether it is measured in my system or in SER).
But the complexity of finding the other puzzle is not defined a priori.

[Added:]If i wanted to program this '2 digits only given in one unit' case, i would replace the givens by the 2 candidates, solve with some techniques, and then for each cell, where only the 2 digits are left as candidates, try one of them. If for one of the cells it's easier to find a solution than for the original (given) cells, the technique makes sense.

No problem with this.
As I remarked previously, this applies to any 2D-cell (i.e. to any bivalue pair of candidates - and of course, trivalue...), not only to the usual units.

[marek stefanik]

You have a given puzzle P1 with some intrinsic rating, say W4 (totally independent of any solver or strategy).
You make some magical trick that transform it into a puzzle P2 with its own intrinsic rating (hopefully) less than that of P1.
Whether you have lost information or not in the process is irrelevant to the question I raised here: http://forum.enjoysudoku.com/eleven-s-variable-replacement-method-and-its-complexity-t39277.html: what's the complexity of the magical trick? Obviously, it can't be less than that of P1.

And... why?
The rating considers some techniques that can solve the puzzle. There is no proof that it is the optimal set of techniques.

It seems to me that you're trying to drive a nail by hitting it with an apple, asking how hard you have to strike it to summon a hammer (in which case calling it a magic trick is understandable).

Marek

[marek stefanik]

I never thought of replacing givens, just candidates. It was a surprise to me, that it can be useful too.

I think that even without replacing the givens there are many cases where you only replace back once the grid has been solved (without any usage of the original givens).
I believe that keeping only one permutation for the solution process is less error-prone, and it makes editing the grid much easier.
Of course, it can sometimes be less powerful (in the 11.7 you can at some point make progress more easily with the original givens, but at that point it is essentially solved anyway).

Marek

[denis_berthier]

You have a given puzzle P1 with some intrinsic rating, say W4 (totally independent of any solver or strategy).
You make some magical trick that transform it into a puzzle P2 with its own intrinsic rating (hopefully) less than that of P1.
Whether you have lost information or not in the process is irrelevant to the question I raised here: http://forum.enjoysudoku.com/eleven-s-variable-replacement-method-and-its-complexity-t39277.html: what's the complexity of the magical trick? Obviously, it can't be less than that of P1.

And... why?
The rating considers some techniques that can solve the puzzle. There is no proof that it is the optimal set of techniques.

It doesn't depend on the set of rules. I could any rating based on the hardest step. Obviously, if the rating is decreased by the trick, the trick complexity, measured according to the same rating, can only be ≥ to that of the original puzzle.

[marek stefanik]

Obviously, if the rating is decreased by the trick, the trick complexity, measured according to the same rating, can only be ≥ to that of the original puzzle.

'Measured according to the same rating' means nothing in this context.
If your rating tells you how hard you have to hit a nail with an apple, it cannot rate taking a hammer.

I don't know how much this applies to your rating systems, but champagne here posted some puzzles where the SER gets drastically increased by disabling the fish rule (checking with YZF_Sudoku, the 2nd and 5th are hilarious).
I'm curious what you get for whips without subsets.

Marek

[denis_berthier]

Obviously, if the rating is decreased by the trick, the trick complexity, measured according to the same rating, can only be ≥ to that of the original puzzle.

'Measured according to the same rating' means nothing in this context.
If your rating tells you how hard you have to hit a nail with an apple, it cannot rate taking a hammer.

If you hit a nail with an apple and drive it in to some point (probably not very far, unless you are trying to drive it into butter) and then add the hammer to your arsenal, the difference in ratings (measured in mm) will tell you how much using the hammer was useful.

I don't know how much this applies to your rating systems, but champagne here posted some puzzles where the SER gets drastically increased by disabling the fish rule (checking with YZF_Sudoku, the 2nd and 5th are hilarious).
I'm curious what you get for whips without subsets.

If you disable the fish rule, it is no longer the SER !!

Much before this, in my books, I've given similar examples for the rating of puzzles (W rating without Subsets by definition) and with adding them (it is then called the S+W rating).
I've gone much beyond giving specific examples:
- I've proved precise subsumption theorems, stating which cases of Subsets can be replaced by chains;
- I've computed stats. For an up-to-date detailed analysis of the power of Subsets wrt whips, see http://forum.enjoysudoku.com/pattern-based-constraint-satisfaction-2nd-edition-t32567-11.html

#2 and 5 are not that extreme: in S4 vs W7 (W6 resp.).
I've given a much more extreme example of a puzzle solvable by swordfishes but not by whips of any length !!
Generally speaking, I've always had long sections in all my books dealing with such exceptional examples.

All of this is unrelated to my remarks about eleven's method.

[marek stefanik]

I've given a much more extreme example of a puzzle solvable by swordfishes but not by whips of any length !!

Perfect, so swordfish here is

some magical trick that transform it [puzzle P1] into a puzzle P2 with its own intrinsic rating (hopefully) less than that of P1. [...]
what's the complexity of the magical trick? Obviously, it can't be less than that of P1. [really?]

The same way the W rating doesn't tell you anything about subsets it doesn't tell you anything about replacements.
Or what do you think the complexity of subsets is, based on that puzzle?

In my metaphor the nail in the wall is the solution grid, I can't see how that can give you a rating function.
Unless you propose the number of unlocked singles as one, which I don't think would be a good one.

Marek

[denis_berthier]

I've given a much more extreme example of a puzzle solvable by swordfishes but not by whips of any length !!

Perfect, so swordfish here is

some magical trick that transform it [puzzle P1] into a puzzle P2 with its own intrinsic rating (hopefully) less than that of P1. [...]
what's the complexity of the magical trick? Obviously, it can't be less than that of P1. [really?]

The same way the W rating doesn't tell you anything about subsets it doesn't tell you anything about replacements.
Or what do you think the complexity of subsets is, based on that puzzle?

It's somehow different. Fishes have their own complexity. But I agree that the change of complexity their addition to whips implies for a puzzle is not related to their own complexity. That's because the deletion of a single candidate (by any means) can have unpredictable consequences.
Replacements don't have their own complexity. Indeed, they are not even patterns. The only thing we can talk about in their cases is the reduction in complexity they allow on a puzzle. Which is also unpredictable.

[marek stefanik]

Replacements don't have their own complexity. Indeed, they are not even patterns. The only thing we can talk about in their cases is the reduction in complexity they allow on a puzzle. Which is also unpredictable.

I think that's something we can agree on.
Replacements give us information which is not directly available from our pencilmarking, rather than making any deductions from our information as other techniques do.

Marek