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Prediction of Recursive Real-Valued Functions from Finite Examples

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Book cover New Frontiers in Artificial Intelligence (JSAI 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4012))

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

This work is partially supported by Grand-in-Aid for Scientific Research 15700137 and 16500084 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Author information

Authors and Affiliations

  1. Department of Business Administration, The University of Kitakyushu, 802-8577, Kitakyushu, Japan

    Eiju Hirowatari

  2. Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, 820-8502, Japan

    Kouichi Hirata

  3. Faculty of Information Sciences, Hiroshima City University, Hiroshima, 731-3194, Japan

    Tetsuhiro Miyahara

Authors
  1. Eiju Hirowatari
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  2. Kouichi Hirata
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  3. Tetsuhiro Miyahara
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Editor information

Editors and Affiliations

  1. ISIR, Osaka University, 8-1, Mihogaoka, 567-0047, Osaka, Ibaraki, Japan

    Takashi Washio

  2. CREST, Japan Science and Technology Agency, Japan

    Akito Sakurai

  3. Dept. of Information Media, Tokyo Denki University, room 1009, 10th floor, building 11, 2-2, Kandanishikicho, Chiyodaku, 101-8457, Tokyo, Japan

    Katsuto Nakajima

  4. National Institute of Informatics, 2-1-2 Chiyoda-ku, 101-8430, Tokyo, Japan

    Hideaki Takeda

  5. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Satoshi Tojo

  6. Department of ISEE, Kyushu University, 819-0395, Fukuoka, Japan

    Makoto Yokoo

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© 2006 Springer-Verlag Berlin Heidelberg

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Hirowatari, E., Hirata, K., Miyahara, T. (2006). Prediction of Recursive Real-Valued Functions from Finite Examples. In: Washio, T., Sakurai, A., Nakajima, K., Takeda, H., Tojo, S., Yokoo, M. (eds) New Frontiers in Artificial Intelligence. JSAI 2005. Lecture Notes in Computer Science(), vol 4012. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780496_25

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  • DOI: https://doi.org/10.1007/11780496_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35470-3

  • Online ISBN: 978-3-540-35471-0

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