An ALS Toxic Set Update


This post reviews Sysudoku history on the problem of spotting ALS toxic sets, and presents the updated  recommendation in the ALS Toxic Set page just completed for the Guide.  This spotting process, to be referred to here as ALS partnering, will be applied in future reviews, and updates

In sysudokie speak, a restricted set of like valued candidates guaranteed to contain a true candidate, a solution placement, is a toxic set.  “Toxic”, because any outside candidate seeing all members of the set is removed.

In a pair of ALS sharing a restricted common value, the like valued candidates of a different value in both ALS are a toxic set. The expert community uses the term ALS_XZ for this toxic set, understandably because almost all of the ALS toxic sets actually spotted by human solvers are ALS partnered with bi-value cells.  The XZ is a reference to the bv wing of XYZ or WXYZ wings.

The logic of the ALS toxic set, that one of the ALS loses the common value, and becomes locked, is best explained in those general terms.  On the other hand, Sysudoku has struggled with the obvious fact that the complexity of detecting a general ALS toxic set is too much for human solvers to undertake, especially those with the knowledge that methods easily spotted with template aids, like XY chains, fish and coloring, come next.

On my first encounter in July 2012, the Sysudoku remedy was to graphically display all ALS, then comparing all promising pairs. By October 2015,  I was ready to admit defeat, with a compromise, updating the 2012 post to generate one ALS at a time, looking forward in the sequence for promising partners. As an algorithm that saves half the ALS vs. ALS comparisons. Also it means that only the most promising, as a partner of a given ALS, are marked on the grid for testing.

It didn’t work. Over the intervening 2 ½ years and 150 posts, I have found very few ALS toxic set eliminations. My talented friend Gordan Fick, on the other hand, has spotted many for me.  My problem is, being neither a computer or Gordon Fick, I need an explicit signpost procedure, something I can recognize, that leads me to the crucial test, and will lead other ordinaries to find enough ALS_XZ to inspire them.

So now Sysudoku takes a third swing, an ALS_XZ spotting technique, is available in the Guide. I’m just hoping to get on base with ALS Partnering.

This is applying the construction vs. search principle to ALS toxic set.  Rather than looking for two ALS that fit together in the right way, look for possible first ALS components. With each one, you are now engaged in one or more guided constructions that will arrive at an ALS_XZ if it exists.

This prescription was tested with the blog cases, all of which it covers. Then to test evaluate the scanning effort and spotting improvement, the selected review puzzles from Castillo’s Only Extreme Sudoku were scanned immediately after line marking. This confirmed that ALS partnering is a large effort.

As to results, In Only Extreme 218, a regular 671-wing,

 

is duplicated by an ALS_XZ.

 

 

A more significant result occurs in Only Extreme 347. The 6’s are locked in the 3 value BARN, but there are no victims.  Also, this is not a BNS1, the remainder values being 569 and 569. But it’s undeniable that the victim 5 is looking at all 5’s in the two ALS.

Missing this removal in the review is significant as well. It enables a Sue de Coq and avoids a coloring trial.

Although ALS partnering does provide a clearly marked trail to follow, it still takes considerable time per productive ALS_XZ. In the Sysudoku order of battle, it is placed with other bv scan methods, to be  completed  prior to template constructing methods. That avoids the appearance of unnecessary scaffold construction. Aside from that consideration, ALS partnering might be better positioned after coloring.  The time it takes might be better spent on a puzzle actually requiring it.

Next week, a sysudokie version of the case study puzzle in Strmckr’s comment on the April 10 post, and some insights it brings. To bring up comments on a past post, click Comments at the bottom.  Also in the next post, a little more on the WXYZ, and some accounting for our honest differences.

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About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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