Learning Context Free Grammars with the Finite Context Property: A Correction of A. Clark’s Algorithm

  • Hans Leiß
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8612)


A. Clark[2] has shown that the class of languages which have a context-free grammar whose nonterminals can be defined by a finite set of contexts can be identified in the limit, given an enumeration of the language and a test for membership. We show by example that Clark’s algorithm may converge to a grammar that does not define the input language. We review the theoretical background, provide a non-obvious modification of the algorithm and prove its correctness.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Clark, A.: A learnable representation for syntax using residuated lattices. In: de Groote, P., Egg, M., Kallmeyer, L. (eds.) FG 2009. LNCS, vol. 5591, pp. 183–198. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Clark, A.: Learning context free grammars with the syntactic concept lattice. In: Sempere, J.M., García, P. (eds.) ICGI 2010. LNCS (LNAI), vol. 6339, pp. 38–51. Springer, Heidelberg (2010)Google Scholar
  3. 3.
    Harris, Z.S.: From morpheme to utterance. Language 22(3), 161–183 (1946)CrossRefGoogle Scholar
  4. 4.
    Jipsen, P., Tsinakis, C.: A survey of residuated lattices. In: Martinez, J. (ed.) Ordered Algebraic Structures, pp. 19–56. Kluwer (2002)Google Scholar
  5. 5.
    Leiß, H.: Learning CFGs with the finite context property. A note on A. Clark’s algorithm. Universität München, CIS, Manuscript (July 2012)Google Scholar
  6. 6.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)Google Scholar
  7. 7.
    Wurm, C.: Completeness of full Lambek calculus for syntactic concept lattices. In: Morrill, G., Nederhof, M.-J. (eds.) Formal Grammar 2012 and 2013. LNCS, vol. 8036, pp. 126–141. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Yoshinaka, R.: Towards dual approaches for learning context-free grammars based on syntactic concept lattices. In: Mauri, G., Leporati, A. (eds.) DLT 2011. LNCS, vol. 6795, pp. 429–440. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Hans Leiß
    • 1
  1. 1.Centrum für Informations- und SprachverarbeitungUniversität MünchenMünchenGermany

Personalised recommendations