The New Sudoku Players' Forum

[marek stefanik]

Yes, the rest of the page is unfortunately limited to bivalue cells.
I don't think the example is bad.
They provide a DP+2 and correctly identify its eliminations.
The slight problem I see is that it is sukaku-only.

Marek

[denis_berthier]

Denis, your definition is based on a fixed RS and all candidates of the cells.

Yes. DPs are defined in resolution states, like any other pattern.

There cannot be 'something close to a DP, i.e. a DP with additional candidates (guardians)', as you write, because then the DP (without the guardians) would only contain a subset of the cells' candidates and would not be a DP by your definition.

That's only word playing. Call it an almost DP, as I've already seen here.

Consider this puzzle:
...3467896..789125789125346..64375988..951267957268413361872954498513672572694831
The resolution state at the start is the following, where 05 in r1c3 means that 5 is the only candidate, but is not filled in.

Code: Select all

,------------,---------,---------,
| 12  12  05 | 3  4  6 | 7  8  9 |

If you need such nonsense to make an argument, we're not going far.
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[denis_berthier]

Definition: a deadly pattern (S, C) is minimal if there is no strictly smaller deadly pattern, i.e. with smaller S or with fewer candidates in C.

Should be: with more candidates in C. The givens in a DP are its non-candidates, i.e. the complement of the pencilmarks.

Maybe you're confusing a deadly pattern (in a necessarily multi-sol puzzle) with an extended form with guardians, used in a unique puzzle. The number of guardians doesn't count in the definition)

The givens in a DP are its non-candidates, i.e. the complement of the pencilmarks.

I don't know what you call the givens of a DP. In a DP, the candidates in the S cells are possible values. They become the impossible values in an "almost-DP" in a unique puzzle but even so, they still appear as candidates.

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[denis_berthier]

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I wanted to avoid the notion of a footprint in the definition of a DP, but this led me to refer to the solution grids and I'm not satisfied with this (because it's not consistent with my general definition of a pattern).
I'll come back to this later.
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[denis_berthier]

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My previous post was before my second morning tea. Here's the solution to the pattern dilemma.

Reminder: I've always said that a whip is not a pattern. Only a whip[n] is a pattern (for any n > 0). The word "whip" alone refers to a whole family of patterns (in this case a very homogeneous family, but still an infinite family).

Simllarly, a "deadly pattern" is not a pattern. The expression "deadly pattern" refers to a whole family of patterns, e.g. the Sudopedia list, or Blue's much larger list or an even larger list yet to be found.
Each of the "deadly patterns" in those lists is a pattern in my strict, pure logic, sense. (Pragmatic proof: watch each of them individually OR see their code in SudoRules - to be published soon on GitHub.)

What this mean in practice is, it's pointless to look for a general definition of a "deadly pattern" in only pure logic terms. All the definitions I've seen so far explicitly refer to solution grids at some point - and it doesn't matter, precisely because they don't have to be pattern-based. Such definitions are useful for finding "deadly patterns"; that's all we expect of them.
But what's important when it comes to use DPs in pattern-based Sudoku solving is, each of the "deadly patterns" can individually be defined as a pattern (in particular without referring to any solution grid).


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