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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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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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Correspondence to Sylvain Lombardy .

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60133-5

  • Online ISBN: 978-3-319-60134-2

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