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Cardinality constraints or, more generally, weight constraints are wellrecognized as an important extension of answer-set programming. Clearly, allcommon algorithmic tasks related to programs with cardinality or weightconstraints - like checking the consistency of a program - are intractable.Many intractable problems in the area of knowledge representation and reasoninghave been shown to become linear time tractable if the treewidth of theprograms or formulas under consideration is bounded by some constant. The goalof this paper is to apply the notion of treewidth to programs with cardinalityor weight constraints and to identify tractable fragments. It will turn outthat the straightforward application of treewidth to such class of programsdoes not suffice to obtain tractability. However, by imposing furtherrestrictions, tractability can be achieved.

Tractable Answer-Set Programming with Weight Constraints: Bounded Treewidth is not Enough