Journal of the ACM (JACM)
Decomposing constraint satisfaction problems using database techniques
Artificial Intelligence
Closure properties of constraints
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Constraints, consistency and closure
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Unifying Framework for Tractable Constraints
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Determining the Number of Solutions to Binary CSP Instances
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
New tractable constraint classes from old
Exploring artificial intelligence in the new millennium
New Tractable Classes From Old
Constraints
Dichotomies for classes of homomorphism problems involving unary functions
Theoretical Computer Science
The expressive rate of constraints
Annals of Mathematics and Artificial Intelligence
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
The complexity of soft constraint satisfaction
Artificial Intelligence
Recent Results on the Algebraic Approach to the CSP
Complexity of Constraints
Affine systems of equations and counting infinitary logic
Theoretical Computer Science
Tricolorable torus knots are NP-complete
Proceedings of the 47th Annual Southeast Regional Conference
The complexity of soft constraint satisfaction
Artificial Intelligence
Information Sciences: an International Journal
Complexity of conservative constraint satisfaction problems
ACM Transactions on Computational Logic (TOCL)
Quantified constraint satisfaction, maximal constraint languages, and symmetric polymorphisms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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In this paper we explore the links between constraint satisfaction problems and universal algebra. We show that a constraint satisfaction problem instance can be viewed as a pair of relational structures, and the solutions to the problem are then the structure preserving mappings between these two relational structures. We give a number of examples to illustrate how this framework can be used to express a wide variety of combinatorial problems, many of which are not generally considered as constraint satisfaction problems. We also show that certain key aspects of the mathematical structure of constraint satisfaction problems can be precisely described in terms of the notion of a Galois connection, which is a standard notion of universal algebra. Using this result, we obtain an algebraic characterisation of the property of minimality in a constraint satisfaction problem. We also obtain a similar algebraic criterion for determining whether or not a given set of solutions can be expressed by a constraint satisfaction problem with a given structure, or a given set of allowed constraint types.