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An Eilenberg theorem for words on countable ordinals

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Book cover LATIN'98: Theoretical Informatics (LATIN 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1380))

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Abstract

We present in this paper an algebraic approach to the theory of languages of words on countable ordinals. The algebraic structure used, called an Ω1-semigroup, is an adaptation of the one used in the theory of regular languages of Ω-words. We show that finite Ω1-semigroups are equivalent to automata. In particular, the proof gives a new algorithm for determinizing automata on countable ordinals. As in the cases of finite and Ω-words, a syntactic Ω1-semigroup can effectively be associated with any regular language of words on countable ordinals. This result is used to prove an Eilenberg type theorem. There is a one-to-one correspondence between varieties of Ω1-languages and pseudo-varieties of Ω1-semigroups.

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Authors and Affiliations

  1. Institut Gaspard Monge, Université de Marne-la-Vallée, 2, rue de la Butte Verte, F-93166, Noisy-le-Grand Cedex

    Nicolas Bedon & Olivier Carton

Authors
  1. Nicolas Bedon
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  2. Olivier Carton
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Cláudio L. Lucchesi Arnaldo V. Moura

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© 1998 Springer-Verlag Berlin Heidelberg

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Bedon, N., Carton, O. (1998). An Eilenberg theorem for words on countable ordinals. In: Lucchesi, C.L., Moura, A.V. (eds) LATIN'98: Theoretical Informatics. LATIN 1998. Lecture Notes in Computer Science, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054310

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  • DOI: https://doi.org/10.1007/BFb0054310

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64275-6

  • Online ISBN: 978-3-540-69715-2

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