Constraint Satisfaction Problems and Finite Algebras

  title={Constraint Satisfaction Problems and Finite Algebras},
  author={Andrei A. Bulatov and Andrei A. Krokhin and Peter Jeavons},
  booktitle={International Colloquium on Automata, Languages and Programming},
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. In this paper we show that any restricted set of constraint types can be associated with a finite universal algebra. We explore how the computational complexity of a restricted constraint satisfaction problem is connected to properties of the corresponding algebra… 

A new tractable class of constraint satisfaction problems

  • V. Dalmau
  • Mathematics, Computer Science
    Annals of Mathematics and Artificial Intelligence
  • 2005
A new class of problems called para-primal problems, incomparable with the families identified by Feder and Vardi (1998), is introduced and it is proved that any constraint problem in this class is decidable in polynomial time.

The property of being polynomial for Mal’tsev constraint satisfaction problems

A combinatorial constraint satisfaction problem aims at expressing in unified terms a wide spectrum of problems in various branches of mathematics, computer science, and AI. The generalized

The Weak Base Method for Constraint Satisfaction

This thesis develops a method that allows to use a refined Galois correspondence to obtain complexity classifications for constraint satisfaction problems and achieves full classifications of the enumeration problem over the three-element domain.

The weak base method for constraint satisfaction

This thesis develops a method that allows to use a refined Galois correspondence to obtain complexity classifications for constraint satisfaction problems and achieves full classifications of the enumeration problem over the three-element domain.

Combinatorial Proof that Subprojective Constraint Satisfaction Problems are NP-Complete

A new general polynomial-time construction the fibre construction is introduced - which reduces any constraint satisfaction problem CSP(H) to the constraint satisfactionProblem CSP (P), where P is any subprojective relational structure, which provides a starting point for a new combinatorial approach to the NP-completeness part of the conjectured Dichotomy Classification of CSPs.

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.

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.

Locally Finite Constraint Satisfaction Problems

This work argues that locally finite templates, which contain potentially infinitely many finite relations, occur naturally in Descriptive Complexity Theory, and studies CSPs over such templates for both finite and infinite, definable instances.

Periodic Constraint Satisfaction Problems: Tractable Subclasses

  • Hubie Chen
  • Computer Science, Mathematics
  • 2005
This work identifies two broad polynomial-time tractable subclasses of the periodic CSP, a generalization of the constraint satisfaction problem (CSP) that is natural for studying constraint networks consisting of constraints obeying a high degree of regularity or symmetry.

Recognizing frozen variables in constraint satisfaction problems




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.

Tractable Constraints on Ordered Domains

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.

Fast Parallel Constraint Satisfaction

The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

This paper isolates a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit a dichotomy, and explains the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy.

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.

The Logic of Constraint Satisfaction

Constraint Satisfaction from a Deductive Viewpoint

  • W. Bibel
  • Computer Science
    Artif. Intell.
  • 1988