Abstract
Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. To address certain problems in minimal identification for Gödel numberings, Freivalds later considered minimal identification in Kolmogorov Numberings. Kolmogorov numberings are in some sense optimal numberings and have some nice properties. We prove certain hierarchy results for minimal identification in every Kolmogorov numbering. In addition we also compare minimal identification in Gödel numbering versus minimal identification in Kolmogorov numberings.
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References
L. Blum and M. Blum. Toward a mathematical theory of inductive inference. Information and Control, 28:125–155, 1975.
M. Blum. A machine independent theory of the complexity of recursive functions. Journal of the ACM, 14:322–336, 1967.
J. Case. Periodicity in generations of automata. Mathematical Systems Theory, 8:15–32, 1974.
K. Chen. Tradeoffs in Machine Inductive Inference. PhD thesis, SUNY at Buffalo, 1981.
K. Chen. Tradeoffs in inductive inference of nearly minimal sized programs. Information and Control, 52:68–86, 1982.
J. Case and C. Smith. Comparison of identification criteria for machine inductive inference. Theoretical Computer Science, 25:193–220, 1983.
R. Freivalds, M. Karpinski, and C. H. Smith. Co-learning of total recursive functions. In Proceedings of the Seventh Annual Conference on Computational Learning Theory, New Brunswick, New Jersey, pages 190–197. ACM-Press, July 1994.
R. Freivalds. Minimal Gödel numbers and their identification in the limit. Lecture Notes in Computer Science, 32:219–225, 1975.
R. Freivalds. Inductive inference of recursive functions: Qualitative theory. In J. Barzdins and D. Bjorner, editors, Baltic Computer Science. Lecture Notes in Computer Science 502, pages 77–110. Springer-Verlag, 1991.
E. M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967.
J. Hopcroft and J. Ullman. Introduction to Automata Theory Languages and Computation. Addison-Wesley Publishing Company, 1979.
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.
H. Rogers. Theory of Recursive Functions and Effective Computability. Mc-Graw Hill, New York, 1967. Reprinted by MIT Press, Cambridge, Massachusetts in 1987.
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© 1995 Springer-Verlag Berlin Heidelberg
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Freivalds, R., Jain, S. (1995). Kolmogorov numberings and minimal identification. In: Vitányi, P. (eds) Computational Learning Theory. EuroCOLT 1995. Lecture Notes in Computer Science, vol 904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59119-2_177
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DOI: https://doi.org/10.1007/3-540-59119-2_177
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