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Learning Deterministic DEC Grammars Is Learning Rational Numbers

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Grammatical Inference: Algorithms and Applications (ICGI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4201))

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Abstract

Below I show that the class of strings that can be learned by a deterministic DEC grammar is exactly the class of rational numbers between 0 and 1. I call this the class of semi-periodic or rational strings. Dynamically Expanding Context (Dec) grammars were introduced by Kohonen in order to model speech signals ([8]). They can be learned in quadratic time in the size of the grammar. They have been used successfully in the automatic generation and analysis of music ([7],[5],[6]).

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References

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Authors and Affiliations

  1. Department of Computer Science, University of Amsterdam, Kruislaan 419, 1098VA, Amsterdam

    Pieter Adriaans

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  1. Pieter Adriaans
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Editors and Affiliations

  1. Department of Biosciences and Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, 223-8522, Yokohama, Japan

    Yasubumi Sakakibara

  2. Dept. of Computer Science, Kyoto Sangyo University, Kamigamo Motoyama, Kita-ku, Kyoto, Japan

    Satoshi Kobayashi

  3. Japan Biological Informatics Consortium, 10F TIME24 Building, 2-45 Aomi, Koto-ku, 135-8073, Tokyo, Japan

    Kengo Sato

  4. Department of Information and Communication Engineering, Graduate School of Electro-Communications, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, 182-8585, Tokyo, Japan

    Tetsuro Nishino

  5. Department of Information and Communication Engineering, Faculty of Electro-Communications, The University of Electro-Communications, Chofugaoka 1–5–1, Chofu, 182-8585, Tokyo, Japan

    Etsuji Tomita

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© 2006 Springer-Verlag Berlin Heidelberg

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Adriaans, P. (2006). Learning Deterministic DEC Grammars Is Learning Rational Numbers. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2006. Lecture Notes in Computer Science(), vol 4201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11872436_26

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  • DOI: https://doi.org/10.1007/11872436_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45264-5

  • Online ISBN: 978-3-540-45265-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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