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Learning with higher order additional information

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Algorithmic Learning Theory (AII 1994, ALT 1994)

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References

  1. L. Adleman and M. Blum. Inductive inference and unsolvability. Journal of Symbolic Logic, 56(3):891–900, 1991.

    Google Scholar 

  2. D. Angluin and C. Smith. A survey of inductive inference: Theory and methods. Computing Surveys, 15:237–289, 1983.

    Google Scholar 

  3. J. Barzdin. Two theorems on the limiting synthesis of functions. In Theory of Algorithms and Programs, Latvian State University, Riga, 210:82–88, 1974.

    Google Scholar 

  4. L. Blum and M. Blum. Toward a mathematical theory of inductive inference. Information and Control, 28:125–155, 1975.

    Google Scholar 

  5. G. Baliga, J. Case, and S. Jain. Language learning with some negative information. In K.W. Wagner P. Enjalbert, A. Finkel, editor, Proceedings of the 10th Symposium on Theoretical Aspects of Computer Science, volume 665 of Lecture Notes in Computer Science, pages 672–681. Springer-Verlag, Berlin, Würzburg, Germany, February 1993. Journal version to appear in Journal of Computer and System Sciences.

    Google Scholar 

  6. G. Baliga, J. Case, S. Jain, and M. Suraj. Machine learning of higher order programs. Journal of Symbolic Logic, 59(2):486–500, 1994.

    Google Scholar 

  7. M. Blum. A machine independent theory of the complexity of recursive functions. Journal of the ACM, 14:322–336, 1967.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. P. Cholak, R. Downey, L. Fortnow, W. Gasarch, E. Kinber, M. Kummer, S. Kurtz, and T. Slaman. Degrees of inferability. In Proceedings of the Fifth Annual Workshop on Computational Learning Theory, Pittsburgh, PA, pages 180–192. ACM Press, July 1992.

    Google Scholar 

  11. J. Case, S. Jain, and S. Ngo Manguelle. Refinements of inductive inference by Popperian and reliable machines. Kybernetika, 30:23–52, 1994.

    Google Scholar 

  12. J. Case, S. Jain, and A. Sharma. On learning limiting programs. International Journal of Foundations of Computer Science, 3(1):93–115, 1992.

    Google Scholar 

  13. J. Case and C. Lynes. Machine inductive inference and language identification. In M. Nielsen and E. Schmidt, editors, Proceedings of the 9th International Colloquium on Automata, Languages and Programming, volume 140, pages 107–115. Springer-Verlag, Berlin, 1982.

    Google Scholar 

  14. J. Case and C. Smith. Comparison of identification criteria for machine inductive inference. Theoretical Computer Science, 25:193–220, 1983.

    Google Scholar 

  15. E. deLeeuw, C. Moore, C. Shannon, and N. Shapiro. Computability by probabilistic machines. Automata Studies, Annals of Math. Studies, 34:183–212, 1956.

    Google Scholar 

  16. M. Fulk. A Study of Inductive Inference machines. PhD thesis, SUNY at Buffalo, 1985.

    Google Scholar 

  17. R. Freivalds and R. Wiehagen. Inductive inference with additional information. Electronische Informationverarbeitung und Kybernetik, 15:179–195, 1979.

    Google Scholar 

  18. J. Gill. Probabilistic Turing Machines and Complexity of Computation. PhD thesis, University of California, Berkeley, 1972.

    Google Scholar 

  19. J. Gill. Computational complexity of probabilistic Turing machines. SIAM Journal on Computing, 6:675–695, 1977.

    Google Scholar 

  20. E. Gold. Limiting recursion. Journal of Symbolic Logic, 30:28–48, 1965.

    Google Scholar 

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

    Google Scholar 

  22. J. Hopcroft and J. Ullman. Introduction to Automata Theory Languages and Computation. Addison-Wesley Publishing Company, 1979.

    Google Scholar 

  23. S. Jain and A. Sharma. On the non-existence of maximal inference degrees for language identification. Information Processing Letters, 47-2:81–88, 1993.

    Google Scholar 

  24. R. Klette and R. Wiehagen. Research in the theory of inductive inference by GDR mathematicians — A survey. Information Sciences, 22:149–169, 1980.

    Google Scholar 

  25. N. Lynch, A. Meyer, and M. Fischer. Relativization of the theory of computational complexity. Transactions of the American Mathematical Society, 220:243–287, 1976.

    Google Scholar 

  26. M. Machtey and P. Young. An Introduction to the General Theory of Algorithms. North Holland, New York, 1978.

    Google Scholar 

  27. D. Osherson, M. Stob, and S. Weinstein. Systems that Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge, Mass., 1986.

    Google Scholar 

  28. M. Pleszkoch, G. Gasarch, S. Jain, and R. Solovay. Learning via queries to an oracle, 1990. Submitted for publication.

    Google Scholar 

  29. H. Putnam. Trial and error predicates and the solution to a problem of Mostowski. Journal of Symbolic Logic, 30:49–57, 1965.

    Google Scholar 

  30. H. Rogers. Gödel numberings of partial recursive functions. Journal of Symbolic Logic, 23:331–341, 1958.

    Google Scholar 

  31. H. Rogers. Theory of Recursive Functions and Effective Computability. Mc-Graw Hill, New York, 1967. Reprinted, MIT Press, 1987.

    Google Scholar 

  32. N. Shapiro. Review of “Limiting recursion” by E.M. Gold and “Trial and error predicates and the solution to a problem of Mostowski” by H. Putnam. Journal of Symbolic Logic, 36:342, 1971.

    Google Scholar 

  33. J. Shoenfield. On degrees of unsolvability. Annals of Mathematics, 69:644–653, 1959.

    Google Scholar 

  34. J. Shoenfield. Degrees of Unsolvability. North-Holland, 1971.

    Google Scholar 

  35. R. Soare. Recursively Enumerable Sets and Degrees. Springer-Verlag, 1987.

    Google Scholar 

  36. J. Viksna. Weak inductive inference. In J. Shawe-Taylor, editor, Proceedings of the First European Workshop on Computational Learning Theory. Oxford University Press, London, University of London, Royal Holloway, December 1993.

    Google Scholar 

  37. R. Wiehagen. Zur Theorie der Algorithmischen Erkennung. 1978. Humboldt-Universität, Berlin.

    Google Scholar 

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Setsuo Arikawa Klaus P. Jantke

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© 1994 Springer-Verlag Berlin Heidelberg

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Baliga, G., Case, J. (1994). Learning with higher order additional information. In: Arikawa, S., Jantke, K.P. (eds) Algorithmic Learning Theory. AII ALT 1994 1994. Lecture Notes in Computer Science, vol 872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58520-6_54

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  • DOI: https://doi.org/10.1007/3-540-58520-6_54

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