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

In this paper we investigate the inductive inference of recursive real-valu ed functions from data. A recursive real-valued function is regarded as a c omputable interval mapping. The teaming model we consider in this paper is an extension of Gold's inductive inference. We first introduce some criteri a for successful inductive inference of recursive real-valued functions. Th en we show a recursively enumerable class of recursive real-valued function s which is not inferable in the limit. This should be an interesting contra st to the result by Wiehagen (1976, Elektronische Informations verarbeitung und Kybernetik, Vol. 12, pp. 93-99) that every recursively enumerable subs et of recursive functions from N to N is consistently inferable in the limi t. We also show that every recursively enumerable class of recursive real-v alued functions on a fixed rational interval is consistently inferable in t he limit. Furthermore, we show that our consistent inductive inference coin cides with the ordinary inductive inference, when we deal with recursive re al-valued functions on a fixed closed rational interval. (C) 2001 Elsevier Science B.V. All rights reserved.