The New Sudoku Players' Forum

by **ReCiviliza** » Tue Jul 07, 2020 8:00 am

Hello, civiliza again but with a new user name (forgot old details).

With my old generator effectively lost I am relearning / rebuilding from an earlier archive on Android.

To this end I have (re) incorporated:

X Chains:
single value throughout
No links in cell
Alternating strong and weak links between cells
-a=a-a=a-

XY Chains:
Bivalue cells
Strong links in cells
Weak links between cells
-ab-bc-cd-da-

Is there a name for:
Multi value cells linked by bilocation values
Weak links in cells
Strong links between cells
-amb=bnc=cpd=dqa-
where the main chain is -ab=bc=cd=da-
and mnp & q are arbitrary values used to indicate the cells are not necessarily bivalve.

by **SpAce** » Wed Jul 08, 2020 1:49 am

Hi civiliza,

ReCiviliza wrote:To this end I have (re) incorporated:

X Chains:
single value throughout
No links in cell
Alternating strong and weak links between cells
-a=a-a=a-

Looks good. You can drop the weak link markers at the ends, though. When writing AICs, the idiom is to start and end with a strong link, and then conclude as eliminations any candidates that both end points see:

[a = a - a = a] => -a (sees both end points of the chain)

XY Chains:
Bivalue cells
Strong links in cells
Weak links between cells
-ab-bc-cd-da-

All true, except that the chain doesn't show the strong links. Better:

[(a=b) - (b=c) - (c=d) - (d=a)] => -a

Is there a name for:
Multi value cells linked by bilocation values
Weak links in cells
Strong links between cells

Sounds like you're talking about Almost Hidden (Locked) Sets (AHS), which are the hidden counterpart to Almost Naked (Locked) Sets (ANS). Both are Almost Locked Sets (ALS), though the latter is what people normally mean when they talk about ALSs.

-amb=bnc=cpd=dqa-
where the main chain is -ab=bc=cd=da-
and mnp & q are arbitrary values used to indicate the cells are not necessarily bivalve.

Are 'amb' etc. 3-digit/3-cell locked sets or three candidates in one cell? It's kind of hard to tell from your description, but I'm assuming the former, because the chains wouldn't make much sense with the latter interpretation. In any case, an obvious problem with both chains is that their links don't alternate. An AIC must have strictly alternating strong and weak inferences, and none can be implied. All links must be written explicitly, just like I did with your XY-Chain example.

Assuming the locked set interpretation, this could work as a chain between four Almost Hidden Triples:

[(amb) = (bnc) - (cpd) = (dqa)] => -a (sees all of the 'a's in both locked sets at the end points of the chain)

I just turned the middle link into a weak one to make them alternate. (Note that it doesn't matter at all if the two c's are also strongly linked in the grid, because the chain uses the weak link between them.) I guess it could be called 'AHS-Chain'.

by **ReCiviliza** » Wed Jul 08, 2020 2:42 am

All three examples used were intended to indicate 4 linked cells in say a hook shape

In my mind the first two could be in a common row, the second and third in a common block and the third and fourth in a common column.

Hence the strong links between all of the cells in the third example.

I am aware that sooner or later I am going to have to implement a full AIC but now I am trying to find a complement to the XY Chain (in which the values are strongly linked within each cell and weakly linked between the cells) whereby the values are weakly linked within each cell but strongly linked between the cells.

by **ReCiviliza** » Wed Jul 08, 2020 4:11 am

I guess using SpAce's nomenclature (combined with my interpretation that brackets denominate the contents of a cell)

What I want a name for is:
[(a-b)=(b-c)=(c-d)=(d-a)] => oh! I see the problem now, while b to d is locked in there is no guarantee that either of the end cells will actually have the value a instead of my arbitrary masking value(s). The a's at the ends:are only weakly linked to each other.

Oh well, I can still use my mapWeakVal() routine in the middle of an AIC, I just need to remember that it should not be used to terminate/start a chain.

by **SpAce** » Wed Jul 08, 2020 8:15 pm

ReCiviliza wrote:All three examples used were intended to indicate 4 linked cells in say a hook shape

Ok, thanks for the clarification. My interpretation was wrong, then. No worries, though. Let's take another look.

In my mind the first two could be in a common row, the second and third in a common block and the third and fourth in a common column.

Such a pattern would be an L3-Wing. The 'L' means that it has only biLocal strong links, '3' means it uses three different digits (the other possibilities are L1 and L2), and 'Wing' means it has exactly three strong links. The last part is true about all 'one-letter-wings' (Y,H,W,S,M,L) but not (UVW)XY(Z)-Wings which are ALS-Z patterns (two strongly-linked ALSs). As a chain:

L3-Wing: [a = (a-b) = (b-c) = c] => -a (in last cell), -c (in first cell) if the end-points see each other

Example 1:

Grid 1: Show

L3-Wing: [(1)r2c1 = (1-2)r2c5 = (2-3)r5c5 = (3)r5c1] => -1 r5c1, -3 r2c1

Note that the end-points have different digits, so they can only eliminate from each other -- not externally. To have the same digit at both ends (without the pattern degenerating into a Skyscraper) we need a bit longer chain:

[a = (a-b) = (b-c) = (c-a) = a] => -a (sees both start and end cell)

Example 2:

Grid 2: Show

[(1)r2c1 = (1-2)r2c5 = (2-3)r3c6 = (3-1)r6c6 = (1)r6c3] => -1 r13c3,r45c1

The official name for that pattern is: _xXx_OvErLy_ObNoXiOuS_sUdOkU_tEcHnIqUe_NaMe_xXx123456. I'm not kidding :lol:

Despite 999_Spring's valiant efforts, the boring truth is there are no standard names for most chains longer than three strong links. Worrying about pattern names should be secondary to having a good chain notation anyway, because almost all named patterns can be written as chains (some fishes and other complex patterns excluded). Personally I learned generic chaining first, and only after a considerable while I learned to name some of the found chains too. Names are fun to know, and sometimes ease up communication, but for actual solving they're just as optional as memorizing specific patterns.

Hence the strong links between all of the cells in the third example.

Like I said, when you write a chain (or even think about it), the links must always alternate, no exception. Otherwise the logic doesn't work at all if the AIC is translated into Boolean logic. What might be confusing for chaining novices is that the native strong links (bivalue, bilocal) are in fact hybrid links. It means that they're both strong and weak, so they can be used in either role. When they're used as weak links, it makes no difference that they're also strong, and they're certainly not written as strong links in the chain then. The same is obviously true the other way when they're used as strong links. An AIC only uses one or the other inference type at a time, and the one actually used is written in the chain.

A hybrid link has the property that exactly one of the two linked items must be true. In terms of Boolean logic they represent XOR gates:

(a XOR b) <=> ((a OR b) AND (a NAND b))

The OR part means that they're strong links (at least one true), and the NAND part means they're also weak links (at most one true). Thus you can use a native strong link for either role in an AIC, but never for both simultaneously. Note also that not all strong links are hybrids, which means that some of them you can only use as strong links but not as weak links.

I am aware that sooner or later I am going to have to implement a full AIC but now I am trying to find a complement to the XY Chain (in which the values are strongly linked within each cell and weakly linked between the cells) whereby the values are weakly linked within each cell but strongly linked between the cells.

Did my (theoretical) examples above help at all? If not, make a Google search on "L3-Wing" on this site (and possibly elsewhere). The search functionality on this site doesn't work when the keyword has dashes.

I guess using SpAce's nomenclature (combined with my interpretation that brackets denominate the contents of a cell)

It's almost a standard interpretation. Brackets are indeed used to surround candidates in a cell, but also digits in a group of cells (as in a locked set). When you write symbolic chains with nodes like (amb) it's not possible to know whether you mean a single cell with three candidates or a locked set of three digits in three cells. Such ambiguities should be clarified in text or otherwise. In a real chain that would be clear, of course, because it shows the cells too. In fact, the least ambiguous way to write a single cell with three candidates is (a|m|b) because they're really ORed -- only one of them can be true, not all three.

What I want a name for is:
[(a-b)=(b-c)=(c-d)=(d-a)] => oh! I see the problem now, while b to d is locked in there is no guarantee that either of the end cells will actually have the value a instead of my arbitrary masking value(s).

Well, even if either or both (b,d) do have an 'a' in their cells, they can't eliminate it. Remember that both ends must see the same elimination. The only way b and d could see the same a is if all three are in the same cell. In fact, if b and d were in the same cell (but not the same candidate), it would be a continuous loop with a lot more eliminations. That possibility requires a bit longer chain:

[b = (b-c) = (c-d) = (d-e) = e - loop] => -all other candidates in the four cells

Example 3:

Grid 3: Show

[(2)r2c1 = (2-3)r2c5 = (3-4)r5c5 = (4-5)r5c1 = (5)r2c1 - loop] => -1346789 r2c1, -1456789 r2c5, -1256789 r5c5, -1236789 r5c1

Pretty cool, huh? Based on this, that might be called Strong Ring.

[(a-b)=(b-c)=(c-d)=(d-a)]

The a's at the ends:are only weakly linked to each other.

Correct. Thus you know that at most one of them can be true. While it doesn't give any direct eliminations, it's a bit of new knowledge at least. It's a good skill to learn to read such derived inferences from AICs, so good job for seeing that!

Similarly (and more commonly) we have strong links at both ends of the chain, which means we know the end points are strongly linked to each other (thus at least one must be true). Those two are the only end point configurations I accept: either both strong (idiomatic AIC, preferable) or both weak (the mostly obsolete DNL style). I can't stand it when people write chains with mixed links at the ends, because the Boolean relationship between the end points is then neither OR nor NAND but an implication (which shouldn't normally be mixed with AICs at all).

by **999_Springs** » Thu Jul 09, 2020 1:45 am

SpAce wrote:[(1)r2c1 = (1-2)r2c5 = (2-3)r3c6 = (3-1)r6c6 = (1)r6c3] => -1 r13c3,r45c1

The official name for that pattern is: _xXx_OvErLy_ObNoXiOuS_sUdOkU_tEcHnIqUe_NaMe_xXx123456. I'm not kidding

hahahaha omg i couldn't stop laughing for two minutes straight when i saw this :lol:

ReCiviliza i think i've heard the term bilocation chain (contrasting with the xy-chain) as a general term for what you're trying to describe in the first post, but i don't remember where i got it from

the strong wing term for 4 different valued bilocations in a rectangle is not mine, it comes from tso and/or jeff here

The New Sudoku Players' Forum

AIC Naming Request

AIC Naming Request

Re: AIC Naming Request

Re: AIC Naming Request

Re: AIC Naming Request

Re: AIC Naming Request

Re: AIC Naming Request