On the Parameterized Complexity of Default Logic and Autoepistemic Logic

  • Arne Meier
  • Johannes Schmidt
  • Michael Thomas
  • Heribert Vollmer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7183)

Abstract

We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. in the context of the implication problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic logic and obtain fixed-parameter time and space efficient algorithms for these problems.

On the other hand, we exhibit, for each of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu), unless P=NP.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Arne Meier
    • 1
  • Johannes Schmidt
    • 2
  • Michael Thomas
    • 3
  • Heribert Vollmer
    • 1
  1. 1.Universität HannoverGermany
  2. 2.Université de la MéditerranéeFrance
  3. 3.TWT GmbHGermany

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