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Learning Languages from Positive Data and a Finite Number of Queries

  • Sanjay Jain
  • Efim Kinber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)

Abstract

A computational model for learning languages in the limit from full positive data and a bounded number of queries to the teacher (oracle) is introduced and explored. Equivalence, superset, and subset queries are considered. If the answer is negative, the teacher may provide a counterexample. We consider several types of counterexamples: arbitrary, least counterexamples, and no counterexamples. A number of hierarchies based on the number of queries (answers) and types of answers/ counterexamples is established. Capabilities of learning with different types of queries are compared. In most cases, one or two queries of one type can sometimes do more than any bounded number of queries of another type. Still, surprisingly, a finite number of subset queries is sufficient to simulate the same number of equivalence queries when behaviourally correct  learners do not receive counterexamples and may have unbounded number of errors in almost all conjectures.

Keywords

Target Language Regular Language Positive Data Bounded Number Unbounded Number 
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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References

  1. [AHK93]
    Angluin, D., Hellerstein, L., Karpinski, M.: Learning read-once formulas with queries. Journal of the ACM 40(1), 185–210 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [Ang80]
    Angluin, D.: Finding patterns common to a set of strings. Journal of Computer and System Sciences 21, 46–62 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [Ang87]
    Angluin, D.: Learning regular sets from queries and counter-examples. Information and Computation 75, 87–106 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [Ang88]
    Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1988)Google Scholar
  5. [Ang01]
    Angluin, D.: Queries revisited. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 12–31. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. [Bār74]
    Bārzdiņš, J.: Two theorems on the limiting synthesis of functions. In: Theory of Algorithms and Programs, Latvian State University, vol. 1, pp. 82–88 (1974) (in Russian)Google Scholar
  7. [BCJ95]
    Baliga, G., Case, J., Jain, S.: Language learning with some negative information. Journal of Computer and System Sciences 51(5), 273–285 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [CL82]
    Case, J., Lynes, C.: Machine inductive inference and language identification. In: Nielsen, M., Schmidt, E.M. (eds.) Proceedings of the 9th International Colloquium on Automata, Languages and Programming. LNCS, vol. 140, pp. 107–115. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  9. [CS83]
    Case, J., Smith, C.: Comparison of identification criteria for machine inductive inference. Theoretical Computer Science 25, 193–220 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [GM98]
    Gasarch, W., Martin, G.: Bounded Queries in Recursion Theory. Birkhäuser, Basel (1998)Google Scholar
  11. [Gol67]
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)zbMATHCrossRefGoogle Scholar
  12. [IJ88]
    Ibarra, O., Jiang, T.: Learning regular languages from counterexamples. In: Proceedings of the Workshop on Computational Learning Theory, pp. 337–351. Morgan Kaufmann, San Francisco (1988)Google Scholar
  13. [JK04a]
    Jain, S., Kinber, E.: Learning language from positive data and negative counterexamples. In: Algorithmic Learning Theory: Fifteenth International Conference ALT 2004, Springer, Heidelberg (2004);(to appear)Google Scholar
  14. [JK04b]
    Jain, S., Kinber, E.: Learning languages from positive data and finite number of queries. Technical Report TRC4/04, School of Computing, National University of Singapore (2004)Google Scholar
  15. [JORS99]
    Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, vol. 2. MIT Press, Cambridge (1999)Google Scholar
  16. [Kin92]
    Kinber, E.: Learning a class of regular expressions via restricted subset queries. In: Jantke, K. (ed.) Analogical and Inductive Inference, Proceedings of the Third International Workshop. LNCS (LNAI), vol. 642, pp. 232–243. Springer, Heidelberg (1992)Google Scholar
  17. [LNZ02]
    Lange, S., Nessel, J., Zilles, S.: Learning languages with queries. In: Proceedings of Treffen der GI-Fachgruppe Maschinelles Lernen (FGML), Learning Lab Lower Saxony, Hannover, Germany, pp. 92–99 (2002)Google Scholar
  18. [LZ04a]
    Lange, S., Zilles, S.: Comparison of query learning and gold-style learning in dependence of the hypothesis space. In: Ben-David, S., Case, J., Maruoka, A. (eds.) ALT 2004. LNCS (LNAI), vol. 3244, pp. 99–113. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. [LZ04b]
    Lange, S., Zilles, S.: Replacing limit learners with equally powerful one-shot query learners. In: Shawe-Taylor, J., Singer, Y. (eds.) COLT 2004. LNCS (LNAI), vol. 3120, pp. 155–169. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. [NL00]
    Nessel, J., Lange, S.: Learning erasing pattern languages with queries. In: Arimura, H., Sharma, A.K., Jain, S. (eds.) ALT 2000. LNCS (LNAI), vol. 1968, pp. 86–100. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  21. [OSW86]
    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
  22. [OW82]
    Osherson, D., Weinstein, S.: Criteria of language learning. Information and Control 52, 123–138 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  23. [Rog67]
    Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967); Reprinted by MIT Press in 1987 Google Scholar
  24. [SHA03]
    Sakamoto, H., Hirata, K., Arimura, H.: Learning elementary formal systems with queries. Theoretical Computer Science A 298, 21–50 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  25. [ZL95]
    Zeugmann, T., Lange, S.: A guided tour across the boundaries of learning recursive languages. In: Jantke, K., Lange, S. (eds.) Algorithmic Learning for Knowledge-Based Systems. LNCS (LNAI), vol. 961, pp. 190–258. Springer, Heidelberg (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sanjay Jain
    • 1
  • Efim Kinber
    • 2
  1. 1.School of ComputingNational University of SingaporeSingapore
  2. 2.Department of Computer ScienceSacred Heart UniversityFairfieldU.S.A.

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