Learning Context Free Grammars with the Finite Context Property: A Correction of A. Clark’s Algorithm
A. Clark 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.
KeywordsClosure Operator Residuated Lattice Context Free Grammar Context Property Membership Query
Unable to display preview. Download preview PDF.
- 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
- 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.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.Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)Google Scholar