Bücher von Denis Berthier

"Hierarchical Classifications in Constraint Satisfaction" starts by recalling the main universal classifications of the instances of a finite binary Constraint Satisfaction Problem, defined in previous books by the same author, as well as their first applications to the Sudoku case. It then introduces a software (SHC) specially developed by François Cordoliani to implement them in the Sudoku case. Finally, it analyses in detail the classification results thus obtained and it shows that the short SHC computation times suggest to use it in the ongoing search for the "hardest" puzzles.

CSP-Rules is a generic pattern-based (or rule-based) solver of finite binary Constraint Satisfaction Problems (CSPs). This software is available on GitHub and it includes fully developed applications to various logic puzzles such as Sudoku, Latin Squares (allowing their Pandiagonal variant), Futoshiki, Kakuro, Numbrix, Hidato, Slitherlink and Map Colouring.CSP-Rules produces not only the solution to a CSP (as all the existing CSP solvers) but also a full "resolution path", i.e. a detailed justification for each step; this is a full mathematical proof of the solution. CSP-Rules and the present book are closely related to the author's book "Pattern Based Constraint Satisfaction and Logic Puzzles", where the fundamental theory underlying the approach is presented.This book includes an extended version of the original "Basic User Manual". But it also introduces new powerful generic rules (OR-chains) for taking advantage of almost-contradictory patterns. In particular, it applies these chains to the analysis of a newly discovered pattern (tridagon) and to the classification of a large database of extreme Sudoku puzzles that have it. It also adds the analyses of 630 impossible patterns and explains how to deal with such a large number of patterns. It shows that a handful of them provide almost the same resolution power as the full set. The long final two chapters are written as research notebooks on these very advanced topics.

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