Recursive Functions

Tcs Technical Report Learning Recursive Functions Learning Recursive Functions

Studying the learnability of classes of recursive functions has attracted considerable interest for at least four decades. Starting with Gold’s (1967) model of learning in the limit, many variations, modifications and extensions have been proposed. These models differ in some of the following: the mode of convergence, the requirements intermediate hypotheses have to fulfill, the set of allowed ...

Real Recursive Functions and Real Extensions of Recursive Functions

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to...

Linear Recursive Functions

With the recent trend of analysing the process of computation through the linear logic looking glass, it is well understood that the ability to copy and erase data is essential in order to obtain a Turingcomplete computation model. However, erasing and copying do not need to be explicitly included in Turing-complete computation models: in this paper we show that the class of partial recursive f...

Classifying Recursive Functions

Primitive Recursive Functions

1. Definition of recursive functions. In this paper, we shall consider certain reductions in the recursion scheme for defining primitive recursive functions. Hereafter, we shall refer to such functions simply as recursive functions. In §1, we define what is meant by a recursive function, and also define some recursive functions which will be used. The statement of the principal results of the p...