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Blowing Holes in Various Aspects of Computational Problems, with Applications to Constraint Satisfaction

  • Peter Jonsson
  • Victor Lagerkvist
  • Gustav Nordh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)

Abstract

We consider methods for constructing NP-intermediate problems under the assumption that P ≠ NP. We generalize Ladner’s original method for obtaining NP-intermediate problems by using parameters with various characteristics. In particular, this generalization allows us to obtain new insights concerning the complexity of CSP problems. We begin by fully characterizing the problems that admit NP-intermediate subproblems for a broad and natural class of parameterizations, and extend the result further such that structural CSP restrictions based on parameters that are hard to compute (such as tree-width) are covered. Hereby we generalize a result by Grohe on width parameters and NP-intermediate problems. For studying certain classes of problems, including CSPs parameterized by constraint languages, we consider more powerful parameterizations. First, we identify a new method for obtaining constraint languages Γ such that CSP(Γ) are NP-intermediate. The sets Γ can have very different properties compared to previous constructions (by, for instance, Bodirsky & Grohe) and provides insights into the algebraic approach for studying the complexity of infinite-domain CSPs. Second, we prove that the propositional abduction problem parameterized by constraint languages admits NP-intermediate problems. This settles an open question posed by Nordh & Zanuttini.

Keywords

Polynomial Time Turing Machine Constraint Satisfaction Constraint Satisfaction Problem Computational Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Peter Jonsson
    • 1
  • Victor Lagerkvist
    • 1
  • Gustav Nordh
    • 1
  1. 1.Department of Computer and Information ScienceLinköping UniversitySweden

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