Search results for "μ-recursive function"
showing 2 items of 2 documents
On the inductive inference of recursive real-valued functions
1999
AbstractWe combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.
On the Amount of Nonconstructivity in Learning Recursive Functions
2011
Nonconstructive proofs are a powerful mechanism in mathematics. Furthermore, nonconstructive computations by various types of machines and automata have been considered by e.g., Karp and Lipton [17] and Freivalds [11]. They allow to regard more complicated algorithms from the viewpoint of much more primitive computational devices. The amount of nonconstructivity is a quantitative characterization of the distance between types of computational devices with respect to solving a specific problem. In the present paper, the amount of nonconstructivity in learning of recursive functions is studied. Different learning types are compared with respect to the amount of nonconstructivity needed to lea…