Model-Checking by Infinite Fly-Automata

  • Bruno Courcelle
  • Irène Durand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8080)


We present logic based methods for constructing XP and FPT graph algorithms, parameterized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make it possible to check properties that are not monadic second-order expressible because their states may include counters, so that their set of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. We present tools for constructing easily algorithms by combining predefined automata for basic functions and properties.


Output Function Chromatic Polynomial Syntactic Tree Nondeterministic Automaton Acyclic Coloring 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arnborg, S., Lagergren, J., Seese, D.: Easy problems for tree-decomposable graphs. J. Algorithms 12, 308–340 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Courcelle, B., Mosbah, M.: Monadic second-order evaluations on tree-decomposable graphs. Theor. Comput. Sci. 109, 49–82 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Courcelle, B.: On the model-checking of monadic second-order formulas with edge set quantifications. Discrete Applied Mathematics 160, 866–887 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Courcelle, B., Durand, I.: Automata for the verification of monadic second-order graph properties. J. Applied Logic 10, 368–409 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Courcelle, B., Durand, I.: Computations by fly-automata beyond monadic second-order logic (preprint, June 2013)Google Scholar
  6. 6.
    Courcelle, B., Durand, I.: Infinite transducers on terms denoting graphs In: Proceedings of the 6th European Lisp Symposium, Madrid (June 2013)Google Scholar
  7. 7.
    Courcelle, B., Engelfriet, J.: Graph structure and monadic second-order logic, a language theoretic approach. Encyclopedia of mathematics and its application, vol. 138. Cambridge University Press (June 2012)Google Scholar
  8. 8.
    Courcelle, B., Makowsky, J., Rotics, U.: Linear-time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Syst. 33, 125–150 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Durand, I.: Object enumeration. In: Proceedings of the 5th European LISP Conference, Zadar, Croatia, pp. 43–57 (May 2012)Google Scholar
  10. 10.
    Downey, R., Fellows, M.: Parameterized complexity. Springer (1999)Google Scholar
  11. 11.
    Fellows, M., et al.: On the complexity of some colorful problems parameterized by treewidth. Inf. Comput. 209, 143–153 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Flum, J., Grohe, M.: Parametrized complexity theory. Springer (2006)Google Scholar
  13. 13.
    Frick, M., Grohe, M.: The complexity of first-order and monadic second-order logic revisited. Ann. Pure Appl. Logic 130, 3–31 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Rao, M.: MSOL partitioning problems on graphs of bounded treewidth and clique-width. Theor. Comput. Sci. 377, 260–267 (2007)zbMATHCrossRefGoogle Scholar
  15. 15.
    Reinhardt, K.: The complexity of translating logic to finite automata. In: Grädel, E., Thomas, W., Wilke, T. (eds.) Automata, Logics, and Infinite Games. LNCS, vol. 2500, pp. 231–238. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Veanes, M., Bjørner, N.: Symbolic automata: The toolkit. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 472–477. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bruno Courcelle
    • 1
  • Irène Durand
    • 1
  1. 1.LaBRI, CNRSUniversité Bordeaux-1TalenceFrance

Personalised recommendations