Constraint satisfaction with infinite domains

@inproceedings{Bodirsky2004ConstraintSW,
  title={Constraint satisfaction with infinite domains},
  author={Manuel Bodirsky},
  year={2004}
}
  • M. Bodirsky
  • Published 6 July 2004
  • Computer Science, Mathematics
Many constraint satisfaction problems have a natural formulation as a homomorphism problem. For a fixed relational structure Gamma we consider the following computational problem: Given a structure S with the same relational signature as Gamma, is there a homomorphism from S to Gamma? This problem is known as the constraint satisfaction problem CSP(Gamma) for the so-called template Gamma and is intensively studied for relational structures Gamma with a finite domain. However, many constraint… Expand
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References

SHOWING 1-10 OF 157 REFERENCES
Constraint Satisfaction with Countable Homogeneous Templates
TLDR
It is proved that the primitive positive definable relations over an ω-categorical structure Γ are precisely the relations that are preserved by the polymorphisms of Γ. Expand
Constraint Satisfaction Problems and Finite Algebras
TLDR
It is shown that any restricted set of constraint types can be associated with a finite universal algebra and the result is a dichotomy theorem which significantly generalises Schaefer's dichotomy for the Generalised Satisfiability problem. Expand
Monotone monadic SNP and constraint satisfaction
TLDR
The question whether every problem in CSP is either in P or is NP-complete is posed, and the class of constraint-satisfaction problems with respect to fixed templates is defined. Expand
Classifying the Complexity of Constraints Using Finite Algebras
TLDR
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored. Expand
Quantified Constraints: Algorithms and Complexity
TLDR
This paper considers a more general framework for constraint satisfaction problems which allows arbitrary quantifiers over constrained variables, rather than just existential quantifiers, and shows that the complexity of such extended problems is determined by the surjective polymorphisms of the constraint predicates. Expand
Tractable conservative constraint satisfaction problems
  • A. Bulatov
  • Mathematics, Computer Science
  • 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
TLDR
This work completely characterize conservative constraint languages that give rise to CSP classes solvable in polynomial time, and obtains a complete description of those (directed) graphs H for which the List H-Coloring problem is poynomial time solvable. Expand
Dichotomies for classes of homomorphism problems involving unary functions
TLDR
A dichotomy result is established for the class of non-uniform constraint satisfaction problems where the template is a λ2-structure with the property that the two unary functions involved are the reverse of one another, in that every such problem is either solvable in polynomial-time or NP-complete. Expand
Conjunctive-query containment and constraint satisfaction
TLDR
This paper examines the tractable cases of Boolean constraint-satisfaction problems and shows that they do uniformize, and exhibits three nonuniform tractability results that uniformize and give rise to polynomial-time solvable cases of constraint satisfaction and conjunctive-query containment. Expand
A dichotomy theorem for constraints on a three-element set
  • A. Bulatov
  • Mathematics, Computer Science
  • The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
Every subclass of the CSP defined by a set of allowed constraints is either tractable or NP-complete, and the criterion separating them is that conjectured by Bulatov et al. (2001). Expand
The complexity of maximal constraint languages
TLDR
This paper systematically study the complexity of all maximal constraint languages, that is, languages whose expressive power is just weaker than that of the language of all constraints. Expand
...
1
2
3
4
5
...