Quantified Constraints: Algorithms and Complexity

  title={Quantified Constraints: Algorithms and Complexity},
  author={Ferdinand B{\"o}rner and Andrei A. Bulatov and Peter Jeavons and Andrei A. Krokhin},
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… 

Quantified Constraint Satisfaction, Maximal Constraint Languages, and Symmetric Polymorphisms

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

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

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

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.

Quantified constraint satisfaction and the polynomially generated powers property

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

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

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

The complexity of constraint satisfaction games and QCSP

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.



Closure properties of constraints

This paper investigates the subclasses that arise from restricting the possible constraint types, and shows that any set of constraints that does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition.

The complexity of maximal constraint languages

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.

Equivalence and Isomorphism for Boolean Constraint Satisfaction

This paper considers the problem of determining whether two given constraint satisfaction instances are equivalent and proves a dichotomy theorem by showing that for all finite sets C of constraints, this problem is either polynomial-time solvable or coNP-complete.

Constraint Satisfaction Problems and Finite Algebras

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.

A dichotomy theorem for constraints on a three-element set

  • A. Bulatov
  • Computer Science
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
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).

The complexity of satisfiability problems

An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.

A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas

Characterising Tractable Constraints

Constraint Satisfaction Problems in Non-deterministic Logarithmic Space

  • V. Dalmau
  • Mathematics, Computer Science
  • 2002
A general condition called bounded path duality is identified, that explains all the families of CSPs previously known to be in NL, and it is shown that closure under any operation in the pseudovariety generated by the class of dual discriminator operations is a sufficient condition for bounded pathDuality.

Computers and Intractability: A Guide to the Theory of NP-Completeness

It is proved here that the number ofrules in any irredundant Horn knowledge base involving n propositional variables is at most n 0 1 times the minimum possible number of rules.