Complexity of Answer Set Checking and Bounded Predicate Arities for Non-ground Answer Set Programming

We present new complexity results on answer set checking for non-ground programs under a variety of syntactic restrictions. For several of these problems, the kind of representation of the answer set to be checked is important. In particular, we consider setbased and bitmap-based representations, which are popular in implementations of Answer Set Programming systems. Furthermore, we present new complexity results for various reasoning tasks under the assumption that predicate arities are bounded by some constant. These results imply that in such a setting – which appears to be a reasonable assumption in practice – more efficient implementations than those currently available may be feasible. 1Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Wien, Austria. E-mail: eiter@kr.tuwien.ac.at 2Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Wien, Austria. E-mail: faber@kr.tuwien.ac.at 3Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Wien, Austria. E-mail: michael@kr.tuwien.ac.at 4Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Wien, Austria. E-mail: pfeifer@dbai.tuwien.ac.at 5Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Wien, Austria. E-mail: stefan@kr.tuwien.ac.at Acknowledgements: This work was partially supported by the Austrian Science Fund (FWF) under project Z29-INF as well as the European Commission projects IST-2002-33570 INFOMIX, IST2001-32429 ICONS, and IST-2001-37004 WASP. A preliminary version of this paper appeared in the Proceedings of Answer Set Programming: Advances in Theory and Implementation. Copyright c 2003 by the authors 2 INFSYS RR 1843-03-11

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