A formal definition of what it means for a machine to learn a collection of concepts in an order determined by a finite acyclic digraph of recursive functions is presented. We show that given a labelled graph G=(V, E) representing the learning structure, there are sets S such that in order to learn a program corresponding to some node i, a machine must have precisely learned programs corresponding to all the predecessor nodes.
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- D. Angluin, W.I. Gasarch, C.H. Smith, Training Sequences, Theoretical Computer Science 66 (1989) pp. 255–272.Google Scholar
- D. Angluin, C.H. Smith, Inductive inference: theory and methods, Computing Survey 15 (1983) pp. 237–269.Google Scholar
- J. Case and C. Smith, Comparison of identification criteria for machine inductive inference, Theoretical Computer Science 25 (1983) pp. 193–220.Google Scholar
- N.J. Cutland, Computability: An introduction to recursive function theory, Cambridge University Press (1980).Google Scholar
- R.P. Daley and C.H. Smith, On the complexity of inductive inference, Information and Control 69 (1986) pp. 12–40.Google Scholar
- M.D. Davis, E.J. Weyuker, Computability, Complexity, and Languages, Academic Press (1983).Google Scholar
- E.M. Gold, Language identification in the limit, Information and Control 10 (1967) pp. 447–474.Google Scholar
- D.B. Lenat, E.A. Feigenbaum: On the thresholds of knowledge, Artificial Intelligence 47 (1991) pp. 185–250.Google Scholar
- C.H. Papadimitriou, K. Steiglitz Combinatorial Optimization: Algorithms and Complexity, Prentice Hall (1982).Google Scholar
- H. Rogers, Jr., Theory of Recursive Functions and Effective Computability, The MIT Press (1988).Google Scholar
- Robert I. Soare, Recursively Enumerable Sets and Degrees, Springer-Verlag (1980).Google Scholar