Implementing Courcelle's Theorem in a declarative framework for dynamic programming

Abstract

Many computationally hard problems become tractable if the graph structure underlying the problem instance exhibits small treewidth. A recent approach to put this idea into practice is based on a declarative interface to Answer Set Programming that allows us to specify dynamic programming over tree decompositions in this language, delegating the computation to dedicated solvers. In this article, we prove that this method can be applied to any problem whose fixed-parameter tractability follows from Courcelle's Theorem.