Complex Analogies: Remarks on the Complexity of HDTP

After an introduction to Heuristic-Driven Theory Projection (HDTP) as framework for computational analogy-making, and a compact primer on parametrized complexity theory, we provide a complexity analysis of the key mechanisms underlying HDTP, together with a short discussion of and reflection on the obtained results. Amongst others, we show that restricted higher-order antiunification as currently used in HDTP is W [1]-hard (and thus NP-hard) already for quite simple cases. Also, we obtain W[2]-hardness, and NP-completeness, for the original mechanism used for reducing second-order to first-order antiunifications in the basic version of the HDTP system.