Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Book cover Language and Automata Theory and Applications (LATA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Clark and Yoshinaka have used the term “distributional learning” more loosely in connection with a number of different learning paradims (see [5] for a survey).

  2. 2.

    The present formulations follow [4].

  3. 3.

    It is clear from Ogden’s proof that the lemma is really about one particular derivation tree of a context-free grammar. If p is the constant of Ogden’s lemma for G, we obtain the required decomposition of the derivation tree by first marking the initial \(a^p\), then the \(b^p\) preceding \(\#\), and then the \(a^p\) immediately following \(\#\).

References

  1. Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation, and Compiling, vol. I. Prentice-Hall, Englewood Cliffs (1972)

    MATH  Google Scholar 

  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

    Chapter  Google Scholar 

  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, 2013

    Article  MathSciNet  MATH  Google Scholar 

  4. Clark, A., Kanazawa, M., Kobele, G.M., Yoshinaka, R.: Distributional learning of some nonlinear tree grammars. Fundamenta Informaticae 146(4), 339–377 (2016)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Ogden, W.: A helpful result for proving inherent ambiguity. Math. Syst. Theory 2(3), 191–194 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  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

    Chapter  Google Scholar 

  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. 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. 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

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Informatics and SOKENDAI, Tokyo, 101–8430, Japan

    Makoto Kanazawa

  2. Graduate School of Information Sciences, Tohoku University, Sendai, Miyagi, 980–8579, Japan

    Ryo Yoshinaka

Authors
  1. Makoto Kanazawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ryo Yoshinaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Makoto Kanazawa .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Kanazawa, M., Yoshinaka, R. (2017). The Strong, Weak, and Very Weak Finite Context and Kernel Properties. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53733-7_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53732-0

  • Online ISBN: 978-3-319-53733-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation