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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)

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.

Keywords

Rational Cover Finite Automaton Elementary Cycle Deterministic Automaton Elementary Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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