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On the Complexity of Constraint-Based Theory Extraction

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Discovery Science (DS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5808))

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Abstract

In this paper we rule out output polynomial listing algorithms for the general problem of discovering theories for a conjunction of monotone and anti-monotone constraints as well as for the particular subproblem in which all constraints are frequency-based. For the general problem we prove a concrete exponential lower time bound that holds for any correct algorithm and even in cases in which the size of the theory as well as the only previous bound are constant. For the case of frequency-based constraints our result holds unless P = NP. These findings motivate further research to identify tractable subproblems and justify approaches with exponential worst case complexity.

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Authors and Affiliations

  1. Fraunhofer IAIS, Schloss Birlinghoven, Sankt Augustin, Germany

    Mario Boley & Thomas Gärtner

Authors
  1. Mario Boley
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  2. Thomas Gärtner
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Editor information

Editors and Affiliations

  1. Faculty of Economics; Rua Dr. Roberto Frias, University of Porto, 4200-465, Porto, Portugal

    João Gama

  2. DCC-FC, Universidade do Porto, Portugal

    Vítor Santos Costa

  3. LIACC/FEP, Universidade do Porto, Portugal

    Alípio Mário Jorge

  4. LIAAD-INESC Porto L.A./Faculty of Economics, University of Porto, Rua de Ceuta, 118-6, 4050-190, Porto, Portugal

    Pavel B. Brazdil

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Boley, M., Gärtner, T. (2009). On the Complexity of Constraint-Based Theory Extraction. In: Gama, J., Costa, V.S., Jorge, A.M., Brazdil, P.B. (eds) Discovery Science. DS 2009. Lecture Notes in Computer Science(), vol 5808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04747-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-04747-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04746-6

  • Online ISBN: 978-3-642-04747-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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