# Constraint Satisfaction Problems and Finite Algebras

@inproceedings{Bulatov2000ConstraintSP, 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}, year={2000} }

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…

## 139 Citations

### A new tractable class of constraint satisfaction problems

- Mathematics, Computer ScienceAnnals 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

- Mathematics
- 2006

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

- Computer Science, Mathematics
- 2008

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

- Computer Science, Mathematics
- 2008

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

- MathematicsMFCS
- 2007

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

- 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.

### 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.

### Locally Finite Constraint Satisfaction Problems

- Computer Science, Mathematics2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

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

- Computer Science, MathematicsConstraints
- 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

- MathematicsTheor. Comput. Sci.
- 2003

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