Pattern-Based Constraint Satisfaction and Logic Puzzles
(Third Edition)

A unified pattern-based perspective of solving Constraint Satisfaction Problems
and its application to various logic puzzles:
Sudoku, Futoshiki, Kakuro, Numbrix©, Hidato©, Slitherlink

Denis Berthier

book cover

48,31 euros    (paperback, 608 pages, Royal: 6.14" x 9.21" - 15.6 cm x 23.4 cm)

ISBN : 978-1-326-67589-9
Lulu Press, November 2021

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Keywords: Artificial Intelligence, Constraint Satisfaction, Constructive Logic, Logic Puzzles, Sudoku, Futoshiki, Kakuro, Map colouring, Numbrix©, Hidato©, Slitherlink.

 © 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.

     "Pattern-Based Constraint Satisfaction and Logic Puzzles" (Third Edition) is a revised and extended edition of the above.

      In the three 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.

More results about the Sudoku CSP (abstracts from and supplements to "The Hidden Logic of Sudoku")

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