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International Symposium on Mathematical Foundations of Computer Science

MFCS 2002: Mathematical Foundations of Computer Science 2002 pp 471–482Cite as

Derivation of Rational Expressions with Multiplicity

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

This paper introduces a generalization of the partial derivatives of rational expressions, due to Antimirov, to rational expressions with multiplicity. We define the derivation of a rational expression with multiplicity in such a way that the result is a polynomial of expressions. This amounts to interpreting the addition symbol at the upper level in the semiring of coefficients.

Former results of Brzozowski and of Antimirov are then expressed in that framework that allows to deal with rational power series, and automata and expressions with multiplicity as well.

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References

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Author information

Authors and Affiliations

  1. Laboratoire Traitement et Communication de l’Information (CNRS URA 820), Ecole Nationale Supérieure des Télécommunications, 46, rue Barrault, 75634, Paris Cedex 13, France

    Sylvain Lombardy & Jacques Sakarovitch

Authors
  1. Sylvain Lombardy
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  2. Jacques Sakarovitch
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Krzysztof Diks  & Wojciech Rytter  & 

  2. Department of Computer Science, Liverpool University, Peach Street, Liverpool, L69 7ZF, UK

    Wojciech Rytter

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© 2002 Springer-Verlag Berlin Heidelberg

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Lombardy, S., Sakarovitch, J. (2002). Derivation of Rational Expressions with Multiplicity. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_39

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  • DOI: https://doi.org/10.1007/3-540-45687-2_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

  • eBook Packages: Springer Book Archive

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