The Complexity of Satisfaction on Sparse Graphs

  • Anuj Dawar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6478)

Abstract

We consider the complexity of deciding, given a graph G and a formula φ of first-order logic in the language of graphs, whether or not G ⊧ φ. In other words, we are interested in the complexity of the satisfaction relation for first-order logic on graphs. More particularly, we look at the complexity of this problem parameterized by the length of the formula φ. This problem (which is known to be AW[*]-complete) includes as special cases many important graph-theoretic problems, including Independent Set, Dominating Set and complete problems at all levels of the W-hierarchy.

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References

  1. 1.
    Courcelle, B.: Graph rewriting: An algebraic and logic approach. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), pp. 193–242. Elsevier, Amsterdam (1990)Google Scholar
  2. 2.
    Dawar, A.: Homomorphism preservation on quasi-wide classes. J. Computer and System Sciences 76, 324–332 (2009)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Dawar, A., Grohe, M., Kreutzer, S.: Locally excluding a minor. In: Proc. 22nd IEEE Symp. on Logic in Computer Science, pp. 270–279 (2007)Google Scholar
  4. 4.
    Dawar, A., Kreutzer, S.: Domination problems in nowhere-dense classes of graphs. In: FSTTCS 2009, pp. 157–168 (2009)Google Scholar
  5. 5.
    Dvořak, Z., Král, D., Thomas, R.: Deciding first-order properties for sparse graphs. In: FoCS 2010 (to appear, 2010)Google Scholar
  6. 6.
    Nešetřil, J., Ossona de Mendez, P.: First-order properties of nowhere dense structures. Journal of Symbolic Logic 75, 868–887 (2010)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Nešetřil, J., Ossona de Mendez, P.: On nowhere dense graphs. European Journal of Combinatorics (to appear, 2010)Google Scholar
  8. 8.
    Seese, D.: Linear time computable problems and first-order descriptions. Math. Struct. in Comp. Science 6, 505–526 (1996)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Anuj Dawar
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK

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