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)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations