Hybrid Logics and NP Graph Properties

  • Francicleber Martins Ferreira
  • Cibele Matos Freire
  • Mario R. F. Benevides
  • L. Menasché Schechter
  • Ana Teresa Martins
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6642)

Abstract

We show that for each property of graphs \(\mathcal{G}\) in NP there is a sequence φ 1, φ 2, ... of formulas of the full hybrid logic which are satisfied exactly by the frames in \(\mathcal{G}\). Moreover, the size of φ n is bounded by a polynomial. We also show that the same holds for each graph property in the polynomial hierarchy.

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References

  1. 1.
    Areces, C., Blackburn, P., Marx, M.: Hybrid logics: Characterization, interpolation and complexity. Journal of Symbolic Logic 66(3), 977–1010 (2001)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Areces, C., ten Cate, B.: Hybrid logics. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, vol. 3, pp. 821–868. Elsevier Science Ltd., Amsterdam (2007)CrossRefGoogle Scholar
  3. 3.
    Barbosa, V.: An introduction to distributed algorithms. The MIT Press, Cambridge (1996)Google Scholar
  4. 4.
    Benevides, M., Schechter, L.: Using modal logics to express and check global graph properties. Logic Journal of IGPL 17(5), 559 (2009)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Blackburn, P., De Rijke, M., Venema, Y.: Modal logic. Cambridge Univ. Pr., Cambridge (2002)MATHGoogle Scholar
  6. 6.
    Bradfield, J., Stirling, C.: Modal mu-calculi. Handbook of Modal Logic 3, 721–756 (2007)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ebbinghaus, H., Flum, J., Thomas, W.: Mathematical logic. Springer, Heidelberg (1994)CrossRefMATHGoogle Scholar
  8. 8.
    Fagin, R.: Generalized first-order spectra and polynomial-time recognizable sets. In: Karp, R. (ed.) Complexity of Computation. SIAM-AMS Proceedings, vol. 7, pp. 43–73. AMS, Providence (1974)Google Scholar
  9. 9.
    Grädel, E.: Why are modal logics so robustly decidable? In: Paun, G., Rozenberg, G., Salomaa, A. (eds.) Current Trends in Theoretical Computer Science. Entering the 21st Century, pp. 393–408. World Scientific, Singapore (2001)Google Scholar
  10. 10.
    Haken, W., Appel, K., Koch, J.: Every planar map is four colorable. Contemporary Mathematics, vol. 98. American Mathematical Society, Providence (1989)MATHGoogle Scholar
  11. 11.
    Immerman, N.: Descriptive complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  12. 12.
    Lynch, N.: Distributed algorithms. Morgan Kaufmann, San Francisco (1996)MATHGoogle Scholar
  13. 13.
    Papadimitriou, C.: Computational complexity. John Wiley and Sons Ltd., Chichester (2003)MATHGoogle Scholar
  14. 14.
    Robertson, N., Sanders, D., Seymour, P., Thomas, R.: The four-colour theorem. Journal of Combinatorial Theory, Series B 70(1), 2–44 (1997)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Vardi, M.: Why is modal logic so robustly decidable. In: Immerman, N., Kolaitis, P.G. (eds.) Descriptive Complexity and Finite Models. Discrete Mathematics and Theoretical Computer Science, vol. 31, pp. 149–184. American Mathematical Society, Providence (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Francicleber Martins Ferreira
    • 1
  • Cibele Matos Freire
    • 1
  • Mario R. F. Benevides
    • 2
  • L. Menasché Schechter
    • 3
  • Ana Teresa Martins
    • 1
  1. 1.Computer Science DepartmentFederal University of CearáBrazil
  2. 2.COPPE/SystemsFederal University of Rio de JaneiroBrazil
  3. 3.Department of Computer ScienceFederal University of Rio de JaneiroBrazil

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