A comparison of identification criteria for inductive inference of recursive real-valued functions

In this paper we investigate the inductive inference of recursive real-valued functions from data. A recursive real-valued function is regarded as a computable interval mapping. The teaming model we consider in this paper is an extension of Gold's inductive inference. We first introduce some criteria for successful inductive inference of recursive real-valued functions. Then we show a recursively enumerable class of recursive real-valued functions which is not inferable in the limit. This should be an interesting contrast to the result by Wiehagen (1976, Elektronische Informations verarbeitung und Kybernetik, Vol. 12, pp. 93-99) that every recursively enumerable subset of recursive functions from N to N is consistently inferable in the limit. We also show that every recursively enumerable class of recursive real-valued functions on a fixed rational interval is consistently inferable in the limit. Furthermore, we show that our consistent inductive inference coincides with the ordinary inductive inference, when we deal with recursive real-valued functions on a fixed closed rational interval. (C) 2001 Elsevier Science B.V. All rights reserved.