String Extension Learning Using Lattices

  • Anna Kasprzik
  • Timo Kötzing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)


The class of regular languages is not identifiable from positive data in Gold’s language learning model. Many attempts have been made to define interesting classes that are learnable in this model, preferably with the associated learner having certain advantageous properties. Heinz ’09 presents a set of language classes called String Extension (Learning) Classes, and shows it to have several desirable properties.

In the present paper, we extend the notion of String Extension Classes by basing it on lattices and formally establish further useful properties resulting from this extension. Using lattices enables us to cover a larger range of language classes including the pattern languages, as well as to give various ways of characterizing String Extension Classes and its learners. We believe this paper to show that String Extension Classes are learnable in a very natural way, and thus worthy of further study.


Minimum Element Computable Function Inductive Inference Regular Language Language Class 
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.


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  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75, 87–106 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bārzdiņš, J.: Inductive inference of automata, functions and programs. In: Proceedings of the 20th International Congress of Mathematicians, Vancouver, Canada, pp. 455–560 (1974); English translation in American Mathematical Society Translations 2, 109, 107–112 (1977)Google Scholar
  4. 4.
    Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence (1984)Google Scholar
  5. 5.
    Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Case, J., Jain, S., Lange, S., Zeugmann, T.: Incremental concept learning for bounded data mining. Information and Computation 152, 74–110 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    de Brecht, M., Kobayashi, M., Tokunaga, H., Yamamoto, A.: Inferability of closed set systems from positive data. In: Washio, T., Satoh, K., Takeda, H., Inokuchi, A. (eds.) JSAI 2006. LNCS (LNAI), vol. 4384, pp. 265–275. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    de la Higuera, C.: Grammatical Inference. Cambridge University Press, Cambridge (2010) (in Press)zbMATHGoogle Scholar
  9. 9.
    Fernau, H.: Identification of function distinguishable languages. Theoretical Computer Science 290(3) (2003)Google Scholar
  10. 10.
    Fulk, M.: A Study of Inductive Inference Machines. PhD thesis, SUNY at Buffalo (1985)Google Scholar
  11. 11.
    Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)zbMATHCrossRefGoogle Scholar
  12. 12.
    Heinz, J.: String extension learning (2009),
  13. 13.
    Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)Google Scholar
  14. 14.
    Jantke, K.P.: Monotonic and non-monotonic inductive inference. New Generation Computing 8(4) (1991)Google Scholar
  15. 15.
    Lange, S., Wiehagen, R.: Polynomial time inference of arbitrary pattern languages. New Generation Computing 8, 361–370 (1991)zbMATHCrossRefGoogle Scholar
  16. 16.
    Nation, J.: Notes on lattice theory (2009),
  17. 17.
    Osherson, D., Stob, M., Weinstein, S.: Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)Google Scholar
  18. 18.
    Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw Hill, New York (1967); Reprinted by MIT Press, Cambridge, Massachusetts (1987)zbMATHGoogle Scholar
  19. 19.
    Royer, J., Case, J.: Subrecursive Programming Systems: Complexity and Succinctness. In: Research monograph in Progress in Theoretical Computer Science. Birkhäuser, Boston (1994)Google Scholar
  20. 20.
    Weinstein, S.: Private communication at the Workshop on Learnability Theory and Linguistics. University of Western Ontario (1982)Google Scholar
  21. 21.
    Wexler, K., Culicover, P.: Formal Principles of Language Acquisition. MIT Press, Cambridge (1980)Google Scholar
  22. 22.
    Wiehagen, R.: Limes-Erkennung rekursiver Funktionen durch spezielle Strategien. Elektronische Informationsverarbeitung und Kybernetik 12, 93–99 (1976)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Anna Kasprzik
    • 1
  • Timo Kötzing
    • 2
  1. 1.FB IV – Abteilung InformatikUniversität TrierTrierGermany
  2. 2.Department 1: Algorithms and ComplexityMax-Planck-Institut für InformatikSaarbrückenGermany

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