Merging Uniform Inductive Learners

  • Sandra Zilles
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2375)


The fundamental learning model considered here is identification of recursive functions in the limit as introduced by Gold [8], but the concept is investigated on a meta-level. A set of classes of recursive functions is uniformly learnable under an inference criterion I, if there is a single learner, which synthesizes a learner for each of these classes from a corresponding description of the class. The particular question discussed here is how unions of uniformly learnable sets of such classes can still be identified uniformly. Especially unions of classes leading to strong separations of inference criteria in the uniform model are considered. The main result is that for any pair (I, I′) of different inference criteria considered here there exists a fixed set of descriptions of learning problems from I, such that its union with any uniformly I-learnable collection is uniformly I′-learnable, but no longer uniformly I-learnable.


Inference Criterion Recursive Function Inductive Inference Hypothesis Space Uniform Model 
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  1. 1.
    Baliga, G., Case, J., Jain, S., The Synthesis of Language Learners, Information and Computation 152, 16–43 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Barzdin, J., Two Theorems on the Limiting Synthesis of Functions, Theory of Algorithms and Programs, Latvian State University, Riga 210, 82–88 (1974) (in Russian).Google Scholar
  3. 3.
    Barzdin, J., Inductive Inference of Automata, Functions and Programs, in Proc. International Congress of Math., Vancouver, 455–460 (1974).Google Scholar
  4. 4.
    Blum, M., A Machine-Independent Theory of the Complexity of Recursive Functions, Journal of the ACM 14(2), 322–336 (1967).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Case, J., Chen, K., Jain, S., Strong Separation of Learning Classes, Journal of Experimental and Theoretical Artificial Intelligence 4, 281–293 (1992).CrossRefGoogle Scholar
  6. 6.
    Case, J., Smith, C., Comparison of Identification Criteria for Machine Inductive Inference, Theoretical Computer Science 25, 193–220 (1983).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Freivalds, R., Kinber, E. B., Wiehagen, R. (1995), How Inductive Inference Strategies Discover Their Errors, Information and Computation 118, 208–226.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gold, E. M., Language Identification in the Limit, Information and Control 10, 447–474 (1967).CrossRefzbMATHGoogle Scholar
  9. 9.
    Jantke, K.P., Natural Properties of Strategies Identifying Recursive Functions, Elektronische Informationsverarbeitung und Kybernetik 15, 487–496 (1979).MathSciNetzbMATHGoogle Scholar
  10. 10.
    Kapur, S., Bilardi, G., On uniform learnability of language families, Information Processing Letters 44, 35–38 (1992).zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Osherson, D.N., Stob, M., Weinstein, S., Synthesizing Inductive Expertise, Information and Computation 77, 138–161 (1988).zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Rogers, H., Theory of Recursive Functions and Effective Computability, MIT Press, Cambridge, Massachusetts (1987).Google Scholar
  13. 13.
    Wiehagen, R., Zeugmann, T., Learning and Consistency, in K.P. Jantke and S. Lange (Eds.): Algorithmic Learning for Knowledge-Based Systems, LNAI 961, 1–24, Springer-Verlag (1995).Google Scholar
  14. 14.
    Zilles, S., On the Comparison of Inductive Inference Criteria for Uniform Learning of Finite Classes, in N. Abe, R. Khardon, and T. Zeugmann (Eds.): ALT 2001, LNAI 2225, 251–266, Springer-Verlag (2001).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Sandra Zilles
    • 1
  1. 1.Fachbereich InformatikUniversität KaiserslauternKaiserslautern

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