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Prediction of Recursive Real-Valued Functions from Finite Examples

  • Eiju Hirowatari
  • Kouichi Hirata
  • Tetsuhiro Miyahara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4012)

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, \({\sc RealFP}_{\emph I}={\sc RealEx}_{\emph I}\).

Keywords

Closed Interval Approximate Expression Recursive Function Computable Function Inductive Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Eiju Hirowatari
    • 1
  • Kouichi Hirata
    • 2
  • Tetsuhiro Miyahara
    • 3
  1. 1.Department of Business AdministrationThe University of KitakyushuKitakyushuJapan
  2. 2.Department of Artificial IntelligenceKyushu Institute of TechnologyIizukaJapan
  3. 3.Faculty of Information SciencesHiroshima City UniversityHiroshimaJapan

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