Skip to main content
SpringerLink
Log in
Book cover

International Conference on Algorithmic Learning Theory

ALT 2010: Algorithmic Learning Theory pp 285–299Cite as

Solutions to Open Questions for Non-U-Shaped Learning with Memory Limitations

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6331))

Abstract

A U-shape occurs when a learner first learns, then unlearns, and, finally, relearns, some target concept. Within the framework of Inductive Inference, previous results have shown, for example, that U-shapes are unnecessary for explanatory learning, but are necessary for behaviorally correct learning.

This paper solves the following two problems regarding non-U-shaped learning posed in the prior literature.

First, it is shown that there are classes learnable with three memory states that are not learnable non-U-shapedly with any finite number of memory states. This result is surprising, as for learning with one or two memory states, U-shapes are known to be unnecessary.

Secondly, it is shown that there is a class learnable memorylessly with a single feedback query such that this class is not learnable non-U-shapedly memorylessly with any finite number of feedback queries. This result is complemented by the result that any class of infinite languages learnable memorylessly with finitely many feedback queries is so learnable without U-shapes – in fact, all classes of infinite languages learnable with complete memory are learnable memorylessly with finitely many feedback queries and without U-shapes. On the other hand, we show that there is a class of infinite languages learnable memorylessly with a single feedback query, which is not learnable without U-shapes by any particular bounded number of feedback queries.

This is a preview of subscription content, 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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Baliga, J. Case, W. Merkle, F. Stephan, and W. Wiehagen. When unlearning helps. Information and Computation, 206:694-709, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  2. Carey, S.: Face perception: Anomalies of development. In: Strauss, S., Stavy, R. (eds.) U-Shaped Behavioral Growth. Developmental Psychology Series. Academic Press, NY (1982)

    Google Scholar 

  3. Case, J.: Periodicity in generations of automata. Mathematical Systems Theory 8, 15–32 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  4. Case, J.: Infinitary self-reference in learning theory. Journal of Experimental and Theoretical Artificial Intelligence 6, 3–16 (1994)

    Article  MATH  Google Scholar 

  5. Case, J.: The power of vacillation in language learning. SIAM Journal on Computing 28, 1941–1969 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Carlucci, L., Case, J., Jain, S., Stephan, F.: Non-U-shaped vacillatory and team learning. Journal of Computer and System Sciences, Special Issue in Memory of Carl Smith (2007)

    Google Scholar 

  7. Carlucci, L., Case, J., Jain, S., Stephan, F.: Results on memory-limited U-shaped learning. Information and Computation 205, 1551–1573 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Case, J., Jain, S., Lange, S., Zeugmann, T.: Incremental concept learning for bounded data mining. Information and Computation 152, 74–110 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Case, J., Lynes, C.: Machine inductive inference and language identification. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 107–115. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  10. Fulk, M., Jain, S., Osherson, D.: Open problems in Systems That Learn. Journal of Computer and System Sciences 49, 589–604 (1994)

    Article  MathSciNet  Google Scholar 

  11. Freivalds, R., Kinber, E., Smith, C.: On the impact of forgetting on learning machines. Journal of the ACM 42, 1146–1168 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)

    Article  MATH  Google Scholar 

  13. Jain, S., Kinber, E.: Iterative learning from texts and counterexamples using additional information. In: Gavaldà, R., Lugosi, G., Zeugmann, T., Zilles, S. (eds.) ALT 2009. LNCS, vol. 5809, pp. 308–322. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Jain, S., Lange, S., Moelius III, S.E., Zilles, S.: Incremental learning with temporary memory. Theoretical Computer Science 411, 2757–2772 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)

    Google Scholar 

  16. Kinber, E., Stephan, F.: Language learning from texts: Mind changes, limited memory and monotonicity. Information and Computation 123, 224–241 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lange, S., Zeugmann, T.: Incremental learning from positive data. Journal of Computer and System Sciences 53, 88–103 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Marcus, G., Pinker, S., Ullman, M., Hollander, M., Rosen, T.J., Xu, F.: Overregularization in Language Acquisition. In: Monographs of the Society for Research in Child Development, vol. 57(4). University of Chicago Press, Chicago (1992); Includes commentary by H. Clahsen

    Google Scholar 

  19. 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 

  20. Osherson, D., Weinstein, S.: Criteria of language learning. Information and Control 52, 123–138 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  21. Royer, J., Case, J.: Subrecursive Programming Systems: Complexity and Succinctness. In: Research monograph in Progress in Theoretical Computer Science. Birkhäuser, Basel (1994)

    Google Scholar 

  22. Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw Hill, New York (1967); Reprinted by MIT Press, Cambridge, Massachusetts (1987)

    MATH  Google Scholar 

  23. Strauss, S., Stavy, R. (eds.): U-Shaped Behavioral Growth. Developmental Psychology Series. Academic Press, NY (1982)

    Google Scholar 

  24. Taatgen, N.A., Anderson, J.R.: Why do children learn to say broke? A model of learning the past tense without feedback. Cognition 86, 123–155 (2002)

    Article  Google Scholar 

  25. Wexler, K., Culicover, P.: Formal Principles of Language Acquisition. MIT Press, Cambridge (1980)

    Google Scholar 

  26. Wiehagen, R.: Limes-Erkennung rekursiver Funktionen durch spezielle Strategien. Elektronische Informationverarbeitung und Kybernetik 12, 93–99 (1976)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer and Information Sciences, University of Delaware, Newark, DE, 19716-2586, USA

    John Case

  2. Max-Planck-Institut für Informatik, Campus E 1 4, 66123, Saarbrücken, Germany

    Timo Kötzing

Authors
  1. John Case
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Timo Kötzing
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research School of Information Sciences and Engineering, Australian National University and NICTA, 0200, Canberra, ACT, Australia

    Marcus Hutter

  2. Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076, Singapore, Republic of Singapore

    Frank Stephan

  3. Department of Computer Science, University of London, Royal Holloway, TW20 0EX, Egham, Surrey, UK

    Vladimir Vovk

  4. Division of Computer Science, Hokkaido University, , ,, N-14, W-9, Sapporo, 060-0814, Japan

    Thomas Zeugmann

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Case, J., Kötzing, T. (2010). Solutions to Open Questions for Non-U-Shaped Learning with Memory Limitations. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2010. Lecture Notes in Computer Science(), vol 6331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16108-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16108-7_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16107-0

  • Online ISBN: 978-3-642-16108-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation