## AIC building using Graded Equivalence Marking

Advanced methods and approaches for solving Sudoku puzzles

### AIC building using Graded Equivalence Marking

I'm learning this fantastic coloring technique, and using it to learn how to find AICs more consistently. I understand how to build chains whenever a candidate gets marked by opposite sub par marks quite well.

Now, I realized that it is possible to build a loop when coming across a super mark that sees a par mark that then gets promoted. I am wondering, is it is possible to build chains for all of the other promotion rules? And if so, how does one go about doing so? Is it also possible to build AICs whenever we come across a contradiction as well?

I understand that I can let the GEM make the eliminations for me, but I'd like to use it to keep learning more about AIC building. It also feels more rewarding to do so .
swolar

Posts: 5
Joined: 02 October 2022

### Re: AIC building using Graded Equivalence Marking

Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1336
Joined: 05 September 2006

### Re: AIC building using Graded Equivalence Marking

Thanks for the links, but I understand AICs and their logic well enough. Maybe I didn't explain what I was looking for clearly.

I want a tool that helps me analyze a puzzle and find chains more consistently.
I was looking at GEM for its ability to do so, but I am not clear on how I can construct chains after using some of its promotion rules. Particularly, the rule that allows you to promote the last unmarked candidate in a house when all the others are already sub-marked with the same parity.
swolar

Posts: 5
Joined: 02 October 2022

### Re: AIC building using Graded Equivalence Marking

What your asking for is a program that pre generates all the node connections from each starting point
Elimination code walks the list.
...

Gem is a manual version of tree walking strong links. With visual indicates for the branch connection points.

there is no on/off for subdigits in a cell technically from an aic. Perspective its a collection of nodes that's is both ( truth& fasle) at each node.
...
Very few on here use gem markups let alone code it as dosent change what code already does as it makes it more cluttered.
At least in my point of view.

In the preference and setting tabs change find
1 elimination per chain uncheck the box
Change the depth search functions to max
Then use the find all
Hodoku is mostly coded with niceloops logic (which are still. Aics with more clutter)

That should help teach how to spot them more frequently.
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1336
Joined: 05 September 2006

### Re: AIC building using Graded Equivalence Marking

I didn't explain myself clearly again. By "tool" I didn't mean a software or program, but rather a technique that I can use when solving a puzzle to help me analyze it. I am aware that more advanced players can find chains without such techniques, but that is because through experience they have developed their own intuition or heuristics of how to find them. And I wanted to use Graded Equivalence Marking (or some technique like it), to find that intuition for myself.

Using the "find all moves" on hodoku has certainly helped me before, but I still have trouble finding chains that jump around all over the place.
swolar

Posts: 5
Joined: 02 October 2022

### Re: AIC building using Graded Equivalence Marking

Honestly it's not from tools like gem which add extra ticks and crosses to points where chain end. Or change to next didigt should be considered.

knowing how they are constructed that we follow around the grid..

Sector by sector connecting same digit
sector to cell for digit swap.

This ends up being many dead ends or ineffective chains.

For me chain buikding works like this

Use the digit highlight button..
Look for any 1 sector that makes a strong link. Mark these cells with a colour.

Toogle through the next 8 digits and see if their is another.
Strong link overtop either or both endpoints... Mark the end cells and the end cell is the next linking point in the new digit.
Repeat.
If the cells can't be linked for a new digit

Check the peer cells for the same digit and mark the end cell
If not check the peers of each cell for a bivavle that has the same digit.
Mark the cell and the digit chain is using the new digit.
If not end the search
Apply the rules of AIC for eliminations.

Chains that are beyond 3 strong links and 2 weak links which is 3 sectors at most
Take a very long time to find and they aren't fast unless your lucky.

Some people do apply this searching method as bfs and instead of marking all cells uses as both true or false..
they use forcing methods to follow the what if around..
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1336
Joined: 05 September 2006

### Re: AIC building using Graded Equivalence Marking

I'm surprised to hear that basically doing BFS by hand is a viable strategy. I always felt like it was a sort of brute force/last resort kind of method.
Thank you for the replies. Although we've gone a bit off topic, I will still try to figure out how to build AICs using GEM and other similar methods (lite coloring, TDP, full tagging, etc); see if any of them work for me.

StrmCkr wrote: Some people do apply this searching method as bfs and instead of marking all cells uses as both true or false..
they use forcing methods to follow the what if around..

So they use a forcing method, and when they spot an elimination they try to find an AIC that achieves the same thing?
swolar

Posts: 5
Joined: 02 October 2022

### Re: AIC building using Graded Equivalence Marking

Gem tag ect are all doing the same things as normal. Aic searchs do your just adding extra notes where strong links and more notes for section.changes on the same digit that can be linked to it.

Bfs manually as a forcing network can find eliminations of aics as well as other subnets that you cannot replicate.
Backwards walking the on off parts revels the AIC. (or not)

Some coders work this way.

3d.medusa for example is bfs colouring which can be forcing or as aic logic gates I've seen both.

If I Remeber correctly David p bird said his system of gem had limitations and are a guide for strong links to be connected or not to remove more starting positions that have no connection points for same digit

Limitation is that it doesn't have marks for internal digit swap points, or marks for digits that are peers of Bi vavles.

the three ways to form chains:
Same to same digit sector change (has marks for this)
Strong link with interal x spot that changes to new strong link digit
Peer of bivavle with same digit.
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1336
Joined: 05 September 2006

### Re: AIC building using Graded Equivalence Marking

Using GEM I also noticed some of the limitations from that technique.
After reading and trying the other techniques (lite coloring/TDP/etc), I noticed they share similar limitations. Full tagging is its own thing, and I simply don't think it is practical for my use case.

At the end of the day, what I really wanted to know was how to find grouped and ALS AICs more consistently. I followed your suggestion and started playing around with forcing chains, and transforming the result from it into an AIC for eliminations. Now I realize what you meant that all these techniques were doing the same thing; except that I felt forcing chains did it better since they take less to set up. They suit my use case well (finding grouped and ALS AICs) and they even point out type 2 discontinous loops, or whatever the type that confirms a candidate as true rather than eliminating it. For now, I don't see a reason to use GEM and company for my solving. So thanks for the advice, even if it took me a while to get it

What happens to forcing chains with 3 or more paths like triple cell/unit forcing chains? Can they simply not be translated to AICs, or only some times?
swolar

Posts: 5
Joined: 02 October 2022

### Re: AIC building using Graded Equivalence Marking

swolar wrote:What happens to forcing chains with 3 or more paths like triple cell/unit forcing chains? Can they simply not be translated to AICs, or only some times?

No, 3-way chains cannot be constructed/written in basic AIC's.

For 3-way chains most AIC solvers also use 3 lines, so-called Krakens, or they use "nested" AIC's. See e.g. there and next post.

Another possibilty is to use pseudo-AIC's by marking ("remembering") a digit in the chain by a * or similar, which is used later to get another link.
In some cases using & and | (and/or symbols), short 3-way links can be combined to one.
For more complex nets a net can be written in several lines using AIC symbols, which can also point up or down a line.

You can find all of them in the Puzzles section.
eleven

Posts: 2976
Joined: 10 February 2008