Abstract
Constraint Satisfaction Problems (CSPs) offer a powerful framework for representing a great variety of problems. Unfortunately, most of the operations associated with CSPs are NP-hard. As some of these operations must be addressed online, compilation structures for CSPs have been proposed, e.g. finite-state automata and Multivalued Decision Diagrams (MDDs).
The aim of this paper is to draw a compilation map of these structures. We cast all of them as fragments of a more general framework that we call Set-labeled Diagrams (SDs), as they are rooted, directed acyclic graphs with variable-labeled nodes and set-labeled edges; contrary to MDDs and Binary Decision Diagrams, SDs are not required to be deterministic (the sets labeling the edges going out of a node are not necessarily disjoint), ordered nor even read-once.
We study the relative succinctness of different subclasses of SDs, as well as the complexity of classically considered queries and transformations. We show that a particular subset of SDs, satisfying a focusing property, has theoretical capabilities very close to those of Decomposable Negation Normal Forms (DNNFs), although they do not satisfy the decomposability property stricto sensu.
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Niveau, A., Fargier, H., Pralet, C. (2012). Representing CSPs with Set-Labeled Diagrams: A Compilation Map. In: Croitoru, M., Rudolph, S., Wilson, N., Howse, J., Corby, O. (eds) Graph Structures for Knowledge Representation and Reasoning. Lecture Notes in Computer Science(), vol 7205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29449-5_6
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DOI: https://doi.org/10.1007/978-3-642-29449-5_6
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