Constraint Satisfaction Problems with Infinite Templates
نویسنده
چکیده
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 pseudovarieties can be used to study the computational complexity of CSPs with ωcategorical 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.
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