A Comparison of Identification Criteria for Inductive Inference of Recursive Real-Valued Functions

Abstract

In this paper we investigate inductive inference of recursive real-valued functions from data. A recursive real-valued function is regarded as a computable interval mapping, which has been introduced by Hirowatari and Arikawa (1997), and modified by ApsĪtis et al (1998). The learning model we consider in this paper is an extension of the 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) 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.