Distinguishing Pattern Languages with Membership Examples

  • Zeinab Mazadi
  • Ziyuan Gao
  • Sandra Zilles
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)


This article determines two learning-theoretic combinatorial parameters, the teaching dimension and the recursive teaching dimension, for various families of pattern languages over alphabets of varying size. Our results and formal proofs are of relevance to recent studies in computational learning theory as well as in formal language theory.


Formal Language Regular Pattern Pattern Language Alphabet Size Distinct Word 
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.: Finding patterns common to a set of strings. J. Comput. Syst. Sci. 21, 46–62 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Arikawa, S., Miyano, S., Shinohara, A., Kuhara, S., Mukouchi, Y., Shinohara, T.: A machine discovery from amino acid sequences by decision trees over regular patterns. New Generation Comput. 11, 361–375 (1993)CrossRefzbMATHGoogle Scholar
  3. 3.
    Darnstädt, M., Doliwa, T., Simon, H.U., Zilles, S.: Order compression schemes. In: Jain, S., Munos, R., Stephan, F., Zeugmann, T. (eds.) ALT 2013. LNCS, vol. 8139, pp. 173–187. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Doliwa, T., Simon, H.U., Zilles, S.: Recursive teaching dimension, learning complexity, and maximum classes. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds.) Algorithmic Learning Theory. LNCS, vol. 6331, pp. 209–223. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Fernau, H., Schmid, M.L.: Pattern matching with variables: A multivariate complexity analysis. In: Fischer, J., Sanders, P. (eds.) CPM 2013. LNCS, vol. 7922, pp. 83–94. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Freydenberger, D.D., Reidenbach, D.: Bad news on decision problems for patterns. Inf. Comput. 208, 83–96 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Freydenberger, D.D., Reidenbach, D.: Inferring descriptive generalisations of formal languages. J. Comp. Sys. Sci. 79, 622–639 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Geilke, M., Zilles, S.: Learning relational patterns. In: Kivinen, J., Szepesvári, C., Ukkonen, E., Zeugmann, T. (eds.) ALT 2011. LNCS, vol. 6925, pp. 84–98. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Geilke, M., Zilles, S.: Polynomial-time algorithms for learning typed pattern languages. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 277–288. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Goldman, S.A., Kearns, M.J.: On the complexity of teaching. J. Comput. Syst. Sci. 50, 20–31 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Jain, S., Ong, Y.S., Stephan, F.: Regular patterns, regular languages and context-free languages. Inf. Process. Lett. 110, 1114–1119 (2010)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Mazadi, Z.: Learning pattern languages from a small number of helpfully chosen examples, M.Sc. Thesis, University of Regina (2013)Google Scholar
  13. 13.
    Nix, R.P.: Editing by example. ACM Trans. Program. Lang. Syst. 7, 600–621 (1985)CrossRefzbMATHGoogle Scholar
  14. 14.
    Reidenbach, D., Schmid, M.L.: Patterns with bounded treewidth. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 468–479. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Reidenbach, D., Schmid, M.L.: Regular and context-free pattern languages over small alphabets. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 130–141. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Shinohara, A., Miyano, S.: Teachability in computational learning. New Generation Comput. 8, 337–347 (1991)CrossRefzbMATHGoogle Scholar
  17. 17.
    Shinohara, T.: Polynomial time inference of extended regular pattern languages. In: Goto, E., Furukawa, K., Nakajima, R., Nakata, I., Yonezawa, A. (eds.) RIMS 1982. LNCS, vol. 147, pp. 115–127. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  18. 18.
    Zilles, S., Lange, S., Holte, R., Zinkevich, M.: Models of cooperative teaching and learning. J. Mach. Learn. Res. 12, 349–384 (2011)MathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Zeinab Mazadi
    • 1
  • Ziyuan Gao
    • 1
  • Sandra Zilles
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

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