I open this topic to discuss TDP as an alternative to AIC.

I've already exchanged with SpAce and others on this subject but it's all scattered in the forum.

For those who really want to understand my TDP approach, I advise you to refer to the following document in PDF format: http://www.assistant-sudoku.com/Pdf/TDP-anglais.pdf.

On the AIC side, I refer to David P.Bird's basic article: http://forum.enjoysudoku.com/an-aic-primer-t33934.html#p258581 and some comments from SpAce.

In my comparison, I insist a bit more on TDP because I understand that people are not used to my definitions, results and notations, and that it needs some explanations here.

I will compare the two ways of doing things by using the example given by David P. Bird in his article :

- Code: Select all

*----------*----------*----------*

r1 | 12 . . | 23 * * | . . . |

r2 | . . . | . . . | . . . |

r3 | * * * | . . 13 | . . . |

*----------*----------*----------*

1) AIC is written (1=2)r1c1 - (2=3)r1c4 - (3=1)r3c6

Since AIC works in both directions, it is deduced that 1r1c1 and 1r3c1 are strongly related => that all candidates weakly related to 1r1c1 and 1r3c1, i.e. 1r1c56 and 1r3c123, can be eliminated.

2) TDP uses the notion of anti-track P'(1r1c1) = {2r1c1, 3r1c4, 1r3c6,... } constructed, by definition, by looking for the candidates that we would place on the puzzle if 1r1c1 was eliminated, we can write here -1r1c1 -> 2r1c1 -> 3r1c4 -> 1r3c6, ...

This leads, as for the AIC, to the elimination of 1r1c56 and 1r3c123 which see 1r1c1 and 1r3c6 by virtue of the Th2 TDP part1 which I recall "If B is a candidate contained in P'(A), then any candidate C who sees B

and A can be eliminated".

My Comment:

1) AIC is a bidirectional writing alternating strong and weak links. Everything is written that makes its supporters say that AIC is generally more productive than a chain of forcing (David P.Bird).

2) The TDP is a writ of implication which may lead one to think that it is less productive than the AIC in terms of elimination because it would be unidirectional. This is not true, because if an AIC establishes reversible paths between two candidates A (start) and B (finish), then we also have P'(A) -> B and P'(B) -> A which gives the same eliminations.

So I will say that TDP contains AICs and forcing chains, because in addition to incorporating linear chains like AICs, TDP allows chains to be nested like forcing net.

Depending on the reactions (which will certainly not be lacking!) I will develop my arguments for comparison.

Robert