The Cantor-Bendixson Analysis of Finite Trees

  • Christian Wurm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8612)


We present a measure on the structural complexity of finite and infinite trees and provide some first result on its relation to context-free grammars and context-free tree grammars. In particular this measure establishes a relation between the complexity of a language as a set, and the complexity of the objects it contains. We show its precise nature and prove its decidability for the formalisms we consider.


Derivation Tree Complete Path Complete Binary Tree Finite Tree Formal Language Theory 
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  1. 1.
    Berstel, J.: Transductions and Context-free Languages. Teubner, Stuttgart (1979)Google Scholar
  2. 2.
    Engelfriet, J., Schmidt, E.M.: Io and oi. i. J. Comput. Syst. Sci. 15(3), 328–353 (1977)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Fraïssé, R.: Theory of Relations. Studies in logic and the foundations of mathematics, vol 118. North-Holland (1986)Google Scholar
  4. 4.
    Greibach, S.A.: Chains of full AFL’s. Mathematical Systems Theory 4, 231–242 (1970)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Hawkins, J.A.: Efficiency and Complexity in Grammars. Oxford Univ. Pr., Oxford (2004)CrossRefGoogle Scholar
  6. 6.
    Hofbauer, D., Huber, M., Kucherov, G.: Some results on top-context-free tree languages. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 157–171. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  7. 7.
    Kepser, S., Rogers, J.: The equivalence of tree adjoining grammars and monadic linear context-free tree grammars. Journal of Logic, Language and Information 20(3), 361–384 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Kracht, M.: The Mathematics of Language. Studies in Generative Grammar, vol. 63. Mouton de Gruyter, Berlin (2003)CrossRefzbMATHGoogle Scholar
  9. 9.
    Rounds, William C.: Mappings and grammars on trees. Mathematical Systems Theory 4(3), 257–287 (1970)Google Scholar
  10. 10.
    Rubin, S.: Automata presenting structures: A survey of the finite string case. Bulletin of Symbolic Logic 14(2), 169–209 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Seki, H., Matsumura, T., Fujii, M., Kasami, T.: On multiple context–free grammars. Theor. Comp. Sci. 88, 191–229 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Simmons, H.: The extendend Cantor-Bendixson analysis of trees. Algebra Universalis 52, 439–468 (2005)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Christian Wurm
    • 1
  1. 1.Universität DüsseldorfGermany

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