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The Good, the Bad, and the Odd: Cycles in Answer-Set Programs

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New Directions in Logic, Language and Computation (ESSLLI 2010, ESSLLI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7415))

Abstract

Backdoors of answer-set programs are sets of atoms that represent “clever reasoning shortcuts” through the search space. Assignments to backdoor atoms reduce the given program to several programs that belong to a tractable target class. Previous research has considered target classes based on notions of acyclicity where various types of cycles (good and bad cycles) are excluded from graph representations of programs. We generalize the target classes by taking the parity of the number of negative edges on bad cycles into account and consider backdoors for such classes. We establish new hardness results and non-uniform polynomial-time tractability relative to directed or undirected cycles.

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Author information

Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Johannes Klaus Fichte

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  1. Johannes Klaus Fichte
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Editors and Affiliations

  1. Department of Psychology, Stanford University, 420 Jordan Hall, 450 Serra Mall, 94305, Stanford, CA, USA

    Daniel Lassiter

  2. University of Luxembourg, 6, Rue Richard Coudenhove Kalergi, 1359, Luxembourg

    Marija Slavkovik

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Fichte, J.K. (2012). The Good, the Bad, and the Odd: Cycles in Answer-Set Programs. In: Lassiter, D., Slavkovik, M. (eds) New Directions in Logic, Language and Computation. ESSLLI ESSLLI 2010 2011. Lecture Notes in Computer Science, vol 7415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31467-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-31467-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31466-7

  • Online ISBN: 978-3-642-31467-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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