Representing CSPs with Set-Labeled Diagrams: A Compilation Map
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.
KeywordsModel Check Variable Order Constraint Satisfaction Problem Outgoing Edge Label Edge
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