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Parallel Learning of Automatic Classes of Languages

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Book cover Algorithmic Learning Theory (ALT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8776))

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Abstract

We introduce and explore a model for parallel learning of families of languages computable by finite automata. In this model, an algorithmic or automatic learner takes on n different input languages and identifies at least m of them correctly. For finite parallel learning, for large enough families, we establish a full characterization of learnability in terms of characteristic samples of languages. Based on this characterization, we show that it is the difference nā€‰āˆ’ā€‰m, the number of languages which are potentially not identified, which is crucial. Similar results are obtained also for parallel learning in the limit. We consider also parallel finite learnability by finite automata and obtain some partial results. A number of problems for automatic variant of parallel learning remain open.

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References

  1. Austinat, H., Diekert, V., Hertrampf, U., Petersen, H.: Regular frequency computations. Theoretical Computer ScienceĀ 330, 15ā€“20 (2005)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  2. Angluin, D., Gasarch, W., Smith, C.: Training sequences. Theoretical Computer ScienceĀ 66, 255ā€“272 (1989)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  3. Angluin, D.: Inductive inference of formal languages from positive data. Information and ControlĀ 45, 117ā€“135 (1980)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  4. Blumensath, A., GrƤdel, E.: Automatic structures. In: 15th Annual IEEE Symposium on Logic in Computer Science (LICS), pp. 51ā€“62. IEEE Computer Society (2000)

    Google ScholarĀ 

  5. Biegel, R., Gasarch, W., Kinber, E.: Frequency computation and bounded queries. Theoretical Computer ScienceĀ 163, 177ā€“192 (1996)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  6. Balodis, K., Kucevalovs, I., Freivalds, R.: Frequency prediction of functions. In: KotĆ”sek, Z., Bouda, J., ČernĆ”, I., Sekanina, L., Vojnar, T., AntoÅ”, D. (eds.) MEMICS 2011. LNCS, vol.Ā 7119, pp. 76ā€“83. Springer, Heidelberg (2012)

    ChapterĀ  Google ScholarĀ 

  7. Gold, E.M.: Language identification in the limit. Information and ControlĀ 10(5), 447ā€“474 (1967)

    ArticleĀ  MATHĀ  Google ScholarĀ 

  8. Jain, S., Luo, Q., Stephan, F.: Learnability of automatic classes. Journal of Computer and System SciencesĀ 78(6), 1910ā€“1927 (2012)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    Google ScholarĀ 

  10. Kinber, E.: Frequency computations in finite automata. KibernetikaĀ 2, 7ā€“15 (1976) (in Russian); English translation in Cybernetics 12, 179ā€“187

    Google ScholarĀ 

  11. Khoussainov, B., Nerode, A.: Automatic presentations of structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol.Ā 960, pp. 367ā€“392. Springer, Heidelberg (1995)

    ChapterĀ  Google ScholarĀ 

  12. Kinber, E., Smith, C., Velauthapillai, M., Wiehagen, R.: On learning multiple concepts in parallel. Journal of Computer and System SciencesĀ 50, 41ā€“52 (1995)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  13. Lange, S., Zeugmann, T.: Language learning in dependence on the space of hypotheses. In: Proceedings of the Sixth Annual Conference on Computational Learning Theory, pp. 127ā€“136. ACM Press (1993)

    Google ScholarĀ 

  14. Mukouchi, Y.: Characterization of finite identification. In: Jantke, K.P. (ed.) AII 1992. LNCS, vol.Ā 642, pp. 260ā€“267. Springer, Heidelberg (1992)

    ChapterĀ  Google ScholarĀ 

  15. Papadimitriou, C.H.S., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover (1998)

    Google ScholarĀ 

  16. Pitt, L.: Probabilistic inductive inference. Journal of the ACMĀ 36, 383ā€“433 (1989)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  17. Rose, G.: An extended notion of computability. Abstracts of International Congress for Logic, Methodology and Philosophy of Science, p. 14 (1960)

    Google ScholarĀ 

  18. Smith, C.: The power of pluralism for automatic program synthesis. Journal of the ACMĀ 29, 1144ā€“1165 (1982)

    ArticleĀ  MATHĀ  Google ScholarĀ 

  19. Trakhtenbrot, B.: On the frequency of computation of functions. Algebra i LogikaĀ 2, 25ā€“32 (1964)

    Google ScholarĀ 

  20. Wiehagen, R., Freivalds, R., Kinber, E.: On the power of probabilistic strategies in inductive inference. Theoretical Computer ScienceĀ 28, 111ā€“133 (1984)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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Jain, S., Kinber, E. (2014). Parallel Learning of Automatic Classes of Languages. In: Auer, P., Clark, A., Zeugmann, T., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2014. Lecture Notes in Computer Science(), vol 8776. Springer, Cham. https://doi.org/10.1007/978-3-319-11662-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-11662-4_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11661-7

  • Online ISBN: 978-3-319-11662-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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