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International Conference on Implementation and Application of Automata

CIAA 2017: Implementation and Application of Automata pp 163–174Cite as

From Hadamard Expressions to Weighted Rotating Automata and Back

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10329)

Abstract

This paper deals with the conversion of expressions denoting Hadamard series into weighted rotating automata. We prove that any algorithm converting rational series into one-way weighted automata can be extended to provide an algorithm which achieves our goal. We apply this to define the derivation and the follow automata of a Hadamard expression. Our method is also used to extend algorithms which perform the inverse conversion, up to some adjustment in order to fulfill some constraints.

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Fig. 1.
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Notes

  1. 1.

    The formal sum in polynomials of expressions (like in polynomials of positions in the next part) is denoted \(\boxplus \) to avoid any confusion with the sum in expressions or with Hadamard operators.

  2. 2.

    Notice that \(\mathbb {K}\langle \mathsf {pos}(\mathsf {E})\rangle \) is not a semiring, since \(\mathsf {pos}(\mathsf {E})\) is not a monoid; nevertheless, we use the same notations as series for denoting the coefficient of such a linear combination.

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Authors and Affiliations

  1. LaBRI UMR 5800, Université de Bordeaux INP Bordeaux, CNRS, Bordeaux, France

    Louis-Marie Dando & Sylvain Lombardy

Authors
  1. Louis-Marie Dando
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  2. Sylvain Lombardy
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Correspondence to Sylvain Lombardy .

Editor information

Editors and Affiliations

  1. LIGM (UMR 8049), CNRS, Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Arnaud Carayol

  2. LIGM (UMR 8049), Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Cyril Nicaud

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Dando, LM., Lombardy, S. (2017). From Hadamard Expressions to Weighted Rotating Automata and Back. In: Carayol, A., Nicaud, C. (eds) Implementation and Application of Automata. CIAA 2017. Lecture Notes in Computer Science(), vol 10329. Springer, Cham. https://doi.org/10.1007/978-3-319-60134-2_14

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  • DOI: https://doi.org/10.1007/978-3-319-60134-2_14

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