© Denis Berthier. All the material in this page and the pages it gives access to are the property of the author and may not be re-published or re-posted without his prior written permission. |

"Pattern-Based Constraint Satisfaction and Logic
Puzzles" (First Edition) developed a pure logic,
pattern-based perspective of solving the finite Constraint
Satisfaction Problem (CSP), with emphasis on finding the
"simplest" solution. It was the second, revised and
largely extended edition of Constraint
Resolution Theories.
"Pattern-Based Constraint Satisfaction and Logic
Puzzles" (Second Edition) is a revised edition
of the above. It is also extended by a chapter on
Slitherlink.
In both editions, different ways of reasoning with the constraints are formalised by various families of "resolution rules", each of them carrying its own notion of simplicity and allowing to define a universal rating system (meaningful for any finite CSP) for the instances of the CSP. A large part of the book illustrates the power of the approach by applying it to various popular logic puzzles. It provides a unified view of how to model and solve them, even though they involve very different types of constraints: obvious symmetric ones in Sudoku, non-symmetric but transitive ones (inequalities) in Futoshiki, topological and geometric ones in Map colouring, Numbrix ^{©} and
Hidato^{©}, more complex non-binary arithmetic
ones in Kakuro (or Cross Sums) and both non-binary and
non-local ones in Slitherlink. It also shows that the
most familiar techniques for these puzzles can indeed be
understood as mere application-specific presentations of
the general rules.Sudoku is used as the main example throughout the book, making it also an advanced level sequel to The Hidden Logic of Sudoku, the reference book on the theory of Sudoku solving, with: many examples of relationships among different rules and of exceptional situations; comparisons of the resolution potential of various families of rules; detailed statistics of puzzles hardness; analysis of extreme instances. Contents (pdf) Foreword (pdf) Introduction (pdf) Final Remarks (pdf) More results about the Sudoku CSP (abstracts from and supplements to "The Hidden Logic of Sudoku") |