Abstract
The present work deals with language learning from text. It considers universal learners for classes of languages in models of additional information and analyzes their complexity in terms of Turing degrees. The following is shown: If the additional information is given by a set containing at least one index for each language from the class to be learned but no index for any language outside the class then there is a universal learner having the same Turing degree as the inclusion problem for enumerable sets. This result is optimal in the sense that any further learner has the same or higher Turing degree. If the additional information is given by a set which contains exactly the indices of the languages from the class to be learned then there is a computable universal learner. Finally, if the additional information is presented as an upper bound on the size of some grammar that generates the language then a high oracle is necessary and sufficient.
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References
Lenny Adleman and Manuel Blum (1991): Inductive Inference and Unsolvability. Journal of Symbolic Logic 56:891–900.
Dana Angluin (1980): Inductive Inference of Formal Languages from Positive Data. Information and Control 45:117–135.
Ganesh Baliga, John Case and Sanjay Jain (1996): Synthesizing Enumeration Techniques for Language Learning. Proceedings of the Ninth Conference on Computational Learning Theory (COLT) 169–180.
Janis Barzdins and Karlis Podnieks (1973): The Theory of Inductive Inference. Proceedings of the Conference on Mathematical Foundations of Computer Science (MFCS) 9–15.
Leonard Blum and Manuel Blum (1975): Towards a Mathematical Theory of Inductive Inference. Information and Control 28:125–155.
Lance Fortnow, William Gasarch, Sanjay Jain, Efim Kinber, Martin Kummer, Steven Kurtz, Mark Pleszkoch, Theodore Shaman, Robert Solovay and Frank Stephan (1994): Extremes in the Degrees of inferability. Annals of pure and Applied Logic 66:231–276.
Rusins Freivalds and Rolf Wiehagen (1979): Inductive inference with additional information. Elektronische Informationsverarbeitung und Kybernetik 15:179–185.
William Gasarch and Mark Pleszkoch (1989): Learning via queries to an oracle. Proceedings of the Second Annual Conference on Computational Learning Theory (COLT) 214–229.
Mark Gold (1967): Language Identification in the Limit. Information and Control 10:447–474.
Sanjay Jain and Arun Sharma (1993): Learning with the Knowledge of an Upper Bound on Program Size. Information and Computation 102:118–166.
Sanjay Jain and Arun Sharma (1993): On the non-existence of maximal inference degrees for language identification. Information Processing Letters 47:81–88.
Klaus-Peter Jantke (1979): Natural properties of strategies identifying recursive functions. Elektronische Informationsverarbeitung und Kybernetik 15:487–496
Susanne Kaufmann and Frank Stephan (1997): Robust Learning with Infinite Additional Information. To appear at EuroCOLT 1997. Long version is available as: Forschungsberichte Mathematische Logik 23/1996 des Mathematischen Institut an der Universität Heidelberg, 1996.
Hartley Rogers, Jr. (1967): Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Company, New York.
Piergiorgio Odifreddi (1989): Classical Recursion Theory. North-Holland.
Daniel Osherson, Dick de Jongh, Eric Martin and Scott Weinstein (1997): Formal learning theory. in Handbook of Logic and Language, edited by J. van Benthem and A ter Meulen. Elsvier, pp. 737–775.
Daniel Osherson, Michael Stob and Scott Weinstein (1986): Systems that Learn. Bradford — The MIT Press, Cambridge, Massachusetts., Massachusetts.
Daniel Osherson, Michael Stob and Scott Weinstein (1988): Synthesizing inductive expertise, Information and Computation 77(2):138–161.
Daniel Osherson, Michael Stob and Scott Weinstein (1991): A Universal Inductive Inference Machine. Journal of Symbolic Logic 56:661–672.
Robert Soare (1987): Recursively Enumerable Sets and Degrees. Springer-Verlag Heidelberg Heidelberg. *** DIRECT SUPPORT *** A0008123 00012
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Stephan, F.C., Terwijn, S.A. (1997). The complexity of universal text-learners. In: Chlebus, B.S., Czaja, L. (eds) Fundamentals of Computation Theory. FCT 1997. Lecture Notes in Computer Science, vol 1279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036205
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DOI: https://doi.org/10.1007/BFb0036205
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