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Machine learning of higher order programs

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Logical Foundations of Computer Science — Tver '92 (LFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

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Abstract

A generator program for a computable function (by definition) generates an infinite sequence of programs all but finitely many of which compute that function. Machine learning of generator programs for computable functions is studied. To partially motivate these studies, it is shown that, in some cases, interesting global properties for computable functions can be proved from suitable generator programs which can not be proved from any ordinary programs for them. The power (for variants of various learning criteria from the literature) of learning generator programs is compared with the power of learning ordinary programs. The learning power in these cases is also compared to that of learning limiting programs, i.e., programs allowed finitely many mind changes about their correct outputs.

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References

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

    Article  Google Scholar 

  2. J. A. 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. J. Case. Learning machines. In W. Demopoulos and A. Marras, editors, Language Learning and Concept Acquisition. Ablex Publishing Company, 1986.

    Google Scholar 

  7. K. Chen. Tradeoffs in Machine Inductive Inference. PhD thesis, SUNY at Buffalo, 1981.

    Google Scholar 

  8. J. Case, S. Jain, and A. Sharma. On learning limiting programs. International Journal on Foundations of Computer Science, 1992. To appear.

    Google Scholar 

  9. J. Case and C. Lynes. Machine inductive inference and language identification. Lecture Notes in Computer Science, 140:107–115, 1982.

    Google Scholar 

  10. W. Craig. On axiomatizability within a system. Journal of Symbolic Logic, 18:30–32, 1953.

    Google Scholar 

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

    Article  Google Scholar 

  12. S. Feferman. Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae, 49:35–92, 1960.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  17. 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 

  18. 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 

  19. E. Mendelson. Introduction to Mathematical Logic. Brooks-Cole, San Francisco, 1986.

    Google Scholar 

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

    Google Scholar 

  21. 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 

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

    Google Scholar 

  23. J. Royer and J. Case. Intensional Subrecursion and Complexity Theory. Research Notes in Theoretical Science. Pitman Press, being revised for expected publication, 1992.

    Google Scholar 

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

    Google Scholar 

  25. H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw Hill, New York, 1967. Reprinted. MIT Press. 1987.

    Google Scholar 

  26. 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 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  30. R. Wiehagen. Zur Therie der Algrithmischen Erkennung. PhD thesis, Humboldt-Universitat, Berlin, 1978.

    Google Scholar 

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Authors and Affiliations

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

    Ganesh Baliga, John Case, Sanjay Jain & Mandayam Suraj

Authors
  1. Ganesh Baliga
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  2. John Case
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  3. Sanjay Jain
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  4. Mandayam Suraj
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Editor information

Anil Nerode Mikhail Taitslin

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© 1992 Springer-Verlag Berlin Heidelberg

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Baliga, G., Case, J., Jain, S., Suraj, M. (1992). Machine learning of higher order programs. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023859

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  • DOI: https://doi.org/10.1007/BFb0023859

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

  • eBook Packages: Springer Book Archive

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