Constraint satisfaction problems with infinite templates

Abstract

Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a non-uniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ω-categorical. We survey examples of such problems in temporal and spatial reasoning, infinite-dimensional algebra, acyclic colorings in graph theory, artificial intelligence, phylogenetic reconstruction in computational biology, and tree descriptions in computational linguistics. We then give an introduction to the universal-algebraic approach to infinite-domain constraint satisfaction, and discuss how cores, polymorphism clones, and pseudo-varieties can be used to study the computational complexity of CSPs with ω-categorical templates. The theoretical results will be illustrated by examples from the mentioned application areas. We close with a series of open problems and promising directions of future research. © 2008 Springer Berlin Heidelberg.