Nick70 wrote:Tabling has been described here.

It is a further generalization of simple forcing chains, more powerful because it can concatenate them.

... the details of the algorithm haven't been published yet.

In fact, there version of Mad Overlord's Sudoku Susser for Wimdows, Mac and Linux downloadable from http://www.madoverlord.com/projects/sudoku.t

It's an excellent piece of software which shows just how well it can be done.

Although the full algorithm for tabling hasn't yet been published, you can switch on the option "Show Trebor's Tables" to trace exactly how the algorithm constructs the proof.

When fed on "toughest" it does seem to perform even better than concatenated forcing chains. My "Ultracolouring" solver (which incorporates contradictions and ver(ac)ities) stalled at a position that still seems to require a depth=3 search.

When I fed this partial solution into the Susser and compared the transcript with my Ultracolourer, I was able to see clearly how it manages to make the additional implications necessary to solve the puzzle "logically". It did take me a few false attempts and a few hours, which probably rules it out for those only interested in manual solving.

I'd like to check my results carefully and dicsuss them with Mad Overlord before making them public.

However, I feel that we may be approaching some kind of limit for strictly logical solvers.

Regards

Andrew