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On S-Regular Prefix-Rewriting Systems and Automatic Structures

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Computing and Combinatorics (COCOON 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

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Abstract

Underlying the notion of an automatic structure is that of a synchronously regular (s-regular for short) set of pairs of strings. Accordingly we consider s-regular prefix-rewriting systems showing that even for fairly restricted systems of this form confluence is undecidable in general. Then a close correspondence is established between the existence of an automatic structure that yields a prefix-closed set of unique representatives for a finitely generated monoid and the existence of an s-regular canonical prefix-rewriting system presenting that monoid.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik/Informatik, Universität Kassel, D-34109, Kassel, Germany

    Friedrich Otto

Authors
  1. Friedrich Otto
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Editor information

Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

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© 1999 Springer-Verlag Berlin Heidelberg

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Otto, F. (1999). On S-Regular Prefix-Rewriting Systems and Automatic Structures. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_42

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  • DOI: https://doi.org/10.1007/3-540-48686-0_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

  • eBook Packages: Springer Book Archive

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