Complex Analogies: Remarks on the Complexity of HDTP

  • Robert Robere
  • Tarek Richard Besold
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7691)


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 anti-unification 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 anti-unifications in the basic version of the HDTP system.


Function Symbol Equational Theory Complex Analogy Cognitive Science Society Input Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Robert Robere
    • 1
  • Tarek Richard Besold
    • 2
  1. 1.University of TorontoCanada
  2. 2.Institute of Cognitive ScienceUniversity of OsnabrückGermany

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