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Minimal automaton of a rational cover

  • Formal Languages And Automata
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 267))

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Abstract

A cover is the set of finite factors of a bi-infinite word. It is quite clear that a rational cover is recognized by a trimmed automaton in the following sense : in every state q, there exists a transition beginning in q and a transition ending in q; furthermore every state is an initial and a final state.

We prove here that every rational cover is recognized by a minimal deterministic trimmed automaton Q in the sense of Eilenberg [4] : if B is a deterministic trimmed automaton which recognizes C, there exists a morphism from B to Q (of course Q is unique save on an isomorphism.

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References

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Authors and Affiliations

  1. L.I.T.P. U.E.R. de Math. — Université Paris 7, 2, Place Jussieu, 75251, Paris Cedex O5, France

    D. Beauquier

Authors
  1. D. Beauquier
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Thomas Ottmann

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© 1987 Springer-Verlag Berlin Heidelberg

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Beauquier, D. (1987). Minimal automaton of a rational cover. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_14

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  • DOI: https://doi.org/10.1007/3-540-18088-5_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18088-3

  • Online ISBN: 978-3-540-47747-1

  • eBook Packages: Springer Book Archive

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