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.


Closure Operator Residuated Lattice Context Free Grammar Context Property Membership Query 
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.
    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