Pattern-Based Constraint Satisfaction and Logic Puzzles

TL;DR

This paper presents a unified, logic-based approach to solving various constraint satisfaction problems and logic puzzles, emphasizing the simplicity of solutions through formalized resolution rules and applying it to diverse puzzles like Sudoku and Kakuro.

Contribution

It introduces a pattern-based, formal framework for modeling and solving CSPs and puzzles, unifying different techniques under a common logic-driven perspective.

Findings

Demonstrates the power of resolution rules across various puzzles

Provides detailed analysis of puzzle hardness and solution strategies

Shows that common puzzle techniques are special cases of the general rules

Abstract

Pattern-Based Constraint Satisfaction and Logic Puzzles develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Different ways of reasoning with the constraints are formalised by various families of "resolution rules", each of them carrying its own notion of simplicity. 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, and even much more complex non-binary arithmetic ones in Kakuro (or Cross Sums). 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" (another book by the same author), 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.