Learning Recursive Functions Refutably

Refutable Inductive Inference of Recursive Functions

Learning of recursive functions refutably informally means that for every recursive function, the learning machine has either to learn this function or to refute it, that is to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the m...

On learning of functions refutably

Learning of recursive functions refutably informally means that for every recursive function, the learning machine has either to learn this function or to refute it, that is to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the m...

Refutably Probably Approximately Correct Learning

Learning recursive functions from approximations

This article investigates algorithmic learning, in the limit, of correct programs for recursive functions f from both input output examples of f and several interesting varieties of approximate additional (algorithmic) information about f. Specifically considered, as such approximate additional information about f, are Rose's frequency computations for f and several natural generalizations from...

An approach to intrinsic complexity of uniform learning

Inductive inference is concerned with algorithmic learning of recursive functions. In the model of learning in the limit a learner successful for a class of recursive functions must eventually find a program for any function in the class from a gradually growing sequence of its values. This approach is generalized in uniform learning, where the problem of synthesizing a successful learner for a...