# 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…

## 74 Citations

### Quantified Constraint Satisfaction, Maximal Constraint Languages, and Symmetric Polymorphisms

- Computer Science, LinguisticsSTACS
- 2005

The quantified constraint satisfaction problem (QCSP), a more general framework in which variables can be quantified both universally and existentially, is concerned with and a complete complexity classification of maximal constraint languages is given.

### Relatively quantified constraint satisfaction

- BusinessConstraints
- 2008

This paper gives a complete complexity classification of the cases of the RQCSP where the types of constraints that may appear are specified by a constraint language.

### The Complexity of Problems for Quantified Constraints

- Computer Science, MathematicsTheory of Computing Systems
- 2009

This paper investigates quantified propositional formulas in conjunctive normal form with “clauses” of arbitrary shapes, i.e., consisting of applying arbitrary relations to variables, and determines the complexity of each of these problems depending on the set of relations allowed in the input formulas.

### The Computational Complexity of Quantified Constraint Satisfaction

- Computer Science
- 2004

This dissertation investigates the computational complexity of cases of the QCSP where the types of constraints that may appear are restricted and introduces a new concept for proving QCSP tractability results called collapsibility.

### Recognizing frozen variables in constraint satisfaction problems

- MathematicsTheor. Comput. Sci.
- 2003

### Quantified constraint satisfaction and the polynomially generated powers property

- Mathematics, Computer ScienceICALP
- 2008

This article identifies a new combinatorial property on algebras, the polynomially generated powers (PGP) property, which it is shown is tightly connected to QCSP complexity, and introduces another new property, switchability, which both implies the PGP property and implies positive complexity results on the QCSP.

### Constraint satisfaction with infinite domains

- Mathematics
- 2004

Omega-categoricity is a rather strong model-theoretic assumption on a relational structure, and it can be used to show that many techniques for constraint satisfaction with finite templates extend to omega- categorical templates.

### The Complexity of Quantified Constraint Satisfaction: Collapsibility, Sink Algebras, and the Three-Element Case

- Computer ScienceSIAM J. Comput.
- 2008

The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the…

### Closures and dichotomies for quantified constraints

- MathematicsElectron. Colloquium Comput. Complex.
- 2006

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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