Monte-Carlo inference and its relations to reliable frequency identification

  • Efim Kinber
  • Thomas Zeugmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 380)

Abstract

For EX and BC-type identification Monte-Carlo inference as well as reliable frequency identification on sets of functions are introduced. In particular, we relate the one to the other and characterize Monte-Carlo inference to exactly coincide with reliable frequency identification, on any set ℳ. Moreover, it is shown that reliable EX and BC-frequency inference forms a new discrete hierarchy having the breakpoints 1, 1/2, 1/3, ....

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References

  1. ANGLUIN, D., AND SMITH, C. H. (1989), Inductive inference: theory and methods. Computing Surveys 15, 237–269CrossRefGoogle Scholar
  2. ANGLUIN, D., AND SMITH, C. H. (1986), Formal inductive inference, in Encyclopedia of Artificial Intelligence, (S. Shapiro, Ed.), to app.Google Scholar
  3. BARZDIN, YA. M. (1974), Two theorems on the limiting synthesis of functions, in Theory of Algorithms and Programs I, (Ya. M. Barzdin, Ed.), pp. 82–88, Latvian State University.Google Scholar
  4. Theory of Algorithms and Programs I, II, III, (1974), (1975), (1977) (Ya. M. Barzdin, Ed.). Latvian State University.Google Scholar
  5. BLUM, L. AND BLUM, M. (1975), Toward a mathematical theory of inductive inference. Inform. and Control 28, 122–155.CrossRefGoogle Scholar
  6. CASE, J., AND SMITH, C. H. (1989), Comparison of identification criteria for machine inductive inference. Theo. Comp. Sci. 25, 198–220Google Scholar
  7. DALEY, R. (1986), Towards the development of an analysis of learning algorithms, in Proc. Internat. Workshop of Analogical and Inductive Inference, Wendisch-Rietz, 1986, (K.P. Jantke, Ed.), Lect. Notes Comp. Sci. 265, pp. 1–18.Google Scholar
  8. GOLD, E. M. (1965), Limiting recursion. J. Symbolic Logic 30, 28–48.Google Scholar
  9. KINBER, E. B., AND ZEUGMANN, T. (1985), Inductive inference of almost everywhere correct programs by reliably working strategies. J. Inf. Processing and Cybernetics (EIK) 21, 91–100.Google Scholar
  10. KLETTE; R., AND WIEHAGEN, R. (1980). Research in the theory of inductive inference by GDR mathematicians — a survey. Inf. Sci. 22, 149–169.Google Scholar
  11. MACHTEY, M., AND YOUNG, P. (1978) "An Introduction to the General Theory of Algorithms", North-Holland, New YorkGoogle Scholar
  12. MINICOZZI, E. (1976), Some natural properties of strong-identification in inductive inference. Theo. Comp. Sci. 2, 345–360.CrossRefGoogle Scholar
  13. OSHERSON, D., STOB, M., AND WEINSTEIN, S. (1986), "Systems that Learn" MIT Press, Cambridge.Google Scholar
  14. PITT, L. B. (1984), A characterization of probabilistic inference. In Proc. 25th Annual Symp. Foundations of Comp. Sci., pp. 485–494.Google Scholar
  15. PITT, L. B. (1985), Probabilistic inductive inference. Yale University, YALEU/DCS/TR-400, Ph.D. Thesis.Google Scholar
  16. PODNIEKS, K.M. (1974), Comparing various concepts of function prediction and program synthesis I, in Theory of Algorithms and Programs, (Ya. M. Barzdin, Ed.), pp. 68–81, Latvian State University.Google Scholar
  17. PODNIEKS, K.M. (1975), Comparing various concepts of function prediction and program synthesis II, Theory of Algorithms and Programs, (Ya. M. Barzdin, Ed.), pp. 35–44 Latvian State University.Google Scholar
  18. ROGERS, H. JR. (1967) "Theory of Recursive Functions and Effective Computability", Mc-Graw Hill, New YorkGoogle Scholar
  19. SMITH, C. H. (1982), The power of pluralism for automatic program synthesis. Journal of the ACM 29, 1144–1165.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Efim Kinber
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.Computing CenterLatvian State UniversityRigaU.S.S.R.
  2. 2.Department of MathematicsHumboldt University at BerlinBerlinG.D.R.

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