January 21-25, 2013, ENS Lyon.

Speakers: Manuel Bodirsky, Michael Pinsker.

A Constraint Satisfaction Problem (CSP) is a computational problem where the task is to decide for a given finite set of variables and constraints whether there is an assignment to the variables that satisfies all constraints. Many computational problems in various areas of theoretical computer science can be modeled in this way.

If the variables take their values in some finite domain, there is a rich universal-algebraic theory that describes those constraint languages whose CSP is NP-hard, and those whose CSP is in P. In this course, we present a powerful generalization of this approach to CSPs where the underlying domain is infinite.
After introducing the necessary background in model theory, the course will also cover recent applications of structural Ramsey theory that have led to complexity classification results for large classes of CSPs.

Outline of the course

Monday: Examples of CSPs from Artificial Intelligence. Primitive positive formulas and NP-hardness proofs. Some efficient algorithms. The Feder-Vardi conjecture.

Tuesday: The universal-algebraic approach. The Inv-Pol Galois correspondence. The core of a structure. The tractability conjecture. Cyclic operations. Exercices.

Wednesday: CSPs on infinite domains. Fraïssé limits, the Ryll-Nardzewski theorem. The Inv-Pol correspondence on infinite domains. The topology of simple convergence.  Henson digraphs and other examples.

Thirsday: Introduction to Ramsey theory. Canonical functions. The classification of Graph-SAT problems.

Friday: Open problems, proposals of research projects. Exam and discussion.

Local contact: Pascal Koiran


Registration is free, but there is a limit on the number of participants and it does include neither housing nor meals (though for lunch the attendees will be granted access to the student cafeteria). Registration should be made before Monday, December 3, by clicking on this link and filling in and sending the e-mail form. You shall receive a confirmation as soon as possible.

Alternatively, you can copy/paste and fill the following form and send it by e-mail to research.school.1@gmail.com, with subject “Registration form — research school 3”

First Name:
Last Name:
Position (MSc student, PhD student, researcher, etc.):
E-mail address:

wishes to attend the research school ‘Constraint satisfaction problems’, taking place at ENS Lyon, from Jan. 21 to Jan. 25.