Advertisement

The Strong, Weak, and Very Weak Finite Context and Kernel Properties

  • Makoto KanazawaEmail author
  • Ryo Yoshinaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10168)

Abstract

We identify the properties of context-free grammars that exactly correspond to the behavior of the dual and primal versions of Clark and Yoshinaka’s distributional learning algorithm and call them the very weak finite context/kernel property. We show that the very weak finite context property does not imply Yoshinaka’s weak finite context property, which has been assumed to hold of the target language for the dual algorithm to succeed. We also show that the weak finite context property is genuinely weaker than Clark’s strong finite context property, settling a question raised by Yoshinaka.

Keywords

Grammatical inference and algorithmic learning Distributional learning Finite context property Finite kernel property Context-free languages 

References

  1. 1.
    Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation, and Compiling, vol. I. Prentice-Hall, Englewood Cliffs (1972)zbMATHGoogle 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). doi: 10.1007/978-3-642-15488-1_5 CrossRefGoogle Scholar
  3. 3.
    Clark, A.: The syntactic concept lattice: another algebraic theory of the context-free languages? J. Log. Comput. 25(5), 1203–1229 (2015). First published online: July 30, 2013MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Clark, A., Kanazawa, M., Kobele, G.M., Yoshinaka, R.: Distributional learning of some nonlinear tree grammars. Fundamenta Informaticae 146(4), 339–377 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Clark, A., Yoshinaka, R.: Distributional learning of context-free and multiple context-free grammars. In: Heinz, J., Sempere, J.M. (eds.) Topics in Grammatical Inference, pp. 143–172. Springer, Berlin (2016)CrossRefGoogle Scholar
  6. 6.
    Leiß, H.: Learning context free grammars with the finite context property: a correction of A. Clark’s algorithm. In: Morrill, G., Muskens, R., Osswald, R., Richter, F. (eds.) Formal Grammar 2014. LNCS, vol. 8612, pp. 121–137. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-44121-3_8 Google Scholar
  7. 7.
    Ogden, W.: A helpful result for proving inherent ambiguity. Math. Syst. Theory 2(3), 191–194 (1968)MathSciNetCrossRefzbMATHGoogle 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). doi: 10.1007/978-3-642-22321-1_37 CrossRefGoogle Scholar
  9. 9.
    Yoshinaka, R.: General perspectives on distributionally learnable classes. In: Kuhlmann, M., Kanazawa, M., Kobele, G.M. (eds.) Proceedings of the 14th Meeting on the Mathematics of Language, pp. 87–98. Association for Computational Linguistics, Stroudsburg (2015)Google Scholar
  10. 10.
    Yoshinaka, R.: Learning conjunctive grammars and contextual binary feature grammars. In: Dediu, A.-H., Formenti, E., Martín-Vide, C., Truthe, B. (eds.) LATA 2015. LNCS, vol. 8977, pp. 623–635. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-15579-1_49 Google Scholar
  11. 11.
    Yoshinaka, R., Kanazawa, M.: Distributional learning of abstract categorial grammars. In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS (LNAI), vol. 6736, pp. 251–266. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-22221-4_17 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.National Institute of Informatics and SOKENDAITokyoJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

Personalised recommendations