Minimal automaton of a rational cover

  • D. Beauquier
Formal Languages And Automata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


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.


Rational Cover Finite Automaton Elementary Cycle Deterministic Automaton Elementary Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • D. Beauquier
    • 1
  1. 1.L.I.T.P. U.E.R. de Math. — Université Paris 7Paris Cedex O5France

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