Prediction of recursive real-valued functions from finite examples

Authors:
Eiju Hirowatari;Kouichi Hirata;Tetsuhiro Miyahara
Affiliations:
Department of Business Administration, The University of Kitakyushu, Kitakyushu, Japan;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan;Faculty of Information Sciences, Hiroshima City University, Hiroshima, Japan
Venue:
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
Year:
2006

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Abstract

In this paper, we investigate prediction of recursive real-valued functions from finite examples by extending the framework of inductive inference of recursive real-valued functions to be a more realistic one. First, we propose a finite prediction machine, which is a procedure that requests finite examples of a recursive real-valued function h and a datum of a real number x, and that outputs a datum of h(x). Then, we formulate finite prediction of recursive real-valued functions and investigate the power of it. Furthermore, for a fixed rational closed interval I, we show that the class of all finitely predictable sets of recursive real-valued functions coincides with the class of all inferable sets of recursive real-valued functions in the limit, that is, ${\sc RealFP}_{\emph I}={\sc RealEx}_{\emph I}$.