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Inferring a Rewriting System from Examples

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Discovey Science (DS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1532))

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Abstract

In their previous paper, Mukouchi and Arikawa discussed both refutability and inferability of a hypothesis space from examples. If a target language is a member of the hypothesis space, then an inference machine should identify it in the limit, otherwise it should refute the hypothesis space itself in a finite time. They pointed out the necessity of refutability of a hypothesis space from a view point of machine discovery. Recently,Mukouchi focused sequences of examples successively generated by a certain kind of system. He call such a sequence an observation with time passage, and a sequence extended as long as possible a complete observation. Then the set of all possible complete observations is called a phenomenon of the system

In this paper, we introduce phenomena generated by rewriting systems known as 0L systems and pure grammars, and investigate their inferability in the limit from positive examples as well as refutable inferability from complete examples

First, we show that any phenomenon class generated by 0L systems is inferable in the limit from positive examples. We also show that the phenomenon class generated by pure grammars such that left hand side of each production is not longer than a fixed length is inferable in the limit from positive examples, while the phenomenon class of unrestricted pure grammars is shown not to be inferable. We also obtain the result that the phenomenon class of pure grammars such that the number of productions and that of axioms are not greater than a fixed number is inferable in the limit from positive examples as well as refutably inferable from complete examples

Supported in part by Grant-in-Aid for Scientific Research on Priority Areas No. 10143104 from the Ministry of Education, Science and Culture, Japan.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Information Sciences College of Integrated Arts and Sciences, Osaka Prefecture University, Sakai, Osaka, 599-8531, Japan

    Yasuhito Mukouchi, Ikuyo Yamaue & Masako Sato

Authors
  1. Yasuhito Mukouchi
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  2. Ikuyo Yamaue
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  3. Masako Sato
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Editor information

Editors and Affiliations

  1. Department of Informatics, Kyushu University, Fukuoka, 812-8581, USA

    Setsuo Arikawa

  2. Institute of Scientific and Industrial Research Devision of Intelligent Systems Science, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka, 567-0047, Japan

    Hiroshi Motoda

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© 1998 Springer-Verlag Berlin Heidelberg

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Mukouchi, Y., Yamaue, I., Sato, M. (1998). Inferring a Rewriting System from Examples. In: Arikawa, S., Motoda, H. (eds) Discovey Science. DS 1998. Lecture Notes in Computer Science(), vol 1532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49292-5_9

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  • DOI: https://doi.org/10.1007/3-540-49292-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65390-5

  • Online ISBN: 978-3-540-49292-4

  • eBook Packages: Springer Book Archive

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