My new booklet Hierarchical Classifications in Constraint Satisfaction or [HCCS] is available on lulu.com https://www.lulu.com/shop/denis-berthier/hierarchical-classifications-in-constraint-satisfaction/paperback/product-654rp6d.html?q=denis+berthier&page=1&pageSize=4

It builds on my previous publications and it serves as a theoretical background for the Sudoku Hierarchical Classifier (SHC) developed by François Cordoliani:

(http://forum.enjoysudoku.com/the-sudoku-hierarchical-classifier-shc-t42075.html

https://github.com/denis-berthier/Sudoku_Hierarchical_Classifier).

It explains how to use the universal classifications in the search for the "hardest" puzzles.

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`Table of contents`

1. Universal hierarchical classifications 7

1.1 Introduction and the emblematic 9×9 Sudoku example 7

1.2 Pure logic classifications based on the hardest step 8

1.3 Universal classifications for Constraint Satisfaction Problems 9

1.4 Trial-and-Error: T&E 9

1.5 T&E(n) (iterated Trial-and-Error) and T&E-depth 11

1.6 Braids[p] and T&E(Bp, n) 13

2. Hierarchical classifications in 9×9 Sudoku 15

2.1 Illustrating the hierarchical classifications in 9×9 Sudoku 15

2.2 CSP-Rules and SudoRules 16

2.3 Known classification results in Sudoku 17

2.4 The quest for the “hardest” puzzles 20

3. The Sudoku Hierarchical Classifier 25

3.1 The Sudoku Hierarchical Classifier (SHC) 25

3.2 Comparison of SudoRules and SHC results 26

3.3 How to use the SHC in the search of the hardest puzzles 27

3.4 Checking the contents of your SHC directory 28

3.5 Typical examples of running the SHC 28

3.6 The SHC command line 29

4. Analysis of the hierachical classifications 33

4.1 The standard SHC examples 34

4.2 Analysis of B computations 34

4.3 Analysis of BpB computations and comparison with SER 35

4.4 Analysis of BpBB computations 37

4.5 Analysis of T&E-depth computations 38

5. References 39

5.1 Books 39

5.2 Software 39

5.3 Puzzle collections and their classifications 40

As for the search of the hardest puzzles, the idea of replacing the SER by T&E-depth has already led to hundreds of thousands of new puzzles in T&E(3), "many" of which happen to have high SER.

My idea is, replacing the SER by BpB could lead to "many" new puzzles in T&E(2), "many" of which might have high SER. The existence of the SHC makes the idea realistic.

Maximising BpB within T&E(2) and maximising T&E-depth are independent goals, both with an intrinsic, structural meaning.

As for all my publications, a free pdf version is available on ResearchGate:

https://www.researchgate.net/publication/374508822_Hierarchical_Classifications_in_Constraint_Satisfaction

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