Quantified Constraints: Algorithms and Complexity

@inproceedings{Brner2003QuantifiedCA,
  title={Quantified Constraints: Algorithms and Complexity},
  author={Ferdinand B{\"o}rner and Andrei A. Bulatov and Peter Jeavons and Andrei A. Krokhin},
  booktitle={CSL},
  year={2003}
}
The standard constraint satisfaction problem over an arbitrary finite domain can be expressed as follows: given a first-order sentence consisting of a conjunction of predicates, where all of the variables are existentially quantified, determine whether the sentence is true. This problem can be parameterized by the set of allowed constraint predicates. With each predicate, one can associate certain predicate-preserving operations, called polymorphisms, and the complexity of the parameterized… 

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Closures and dichotomies for quantified constraints

This study studies quantified constraint satisfaction problems CSP(Q,S), where Q denotes a pattern of quantifier alternation ending in exists or the set of all possible alternations of quantifiers, and S is a set of relations constraining the com- binations of values that the variables may take, and establishes three broad sufficient conditions for polynomial-time solvability of CSP 0 (Q) that are based on closure functions.
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