On the equivalence of Z-automata

  • Authors:

  • Marie-Pierre Béal;Sylvain Lombardy;Jacques Sakarovitch

  • Affiliations:

  • Institut Gaspard-Monge, Université Marne-la-Vallée;LIAFA, Université Paris 7;LTCI, CNRS/Ecole Nationale Supérieure des Télécommunications. (UMR 5141)

  • Venue:
  • ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
  • Year:
  • 2005

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Abstract

We prove that two automata with multiplicity in ${\mathbb Z}$ are equivalent, i.e. define the same rational series, if and only if there is a sequence of ${\mathbb Z}$-coverings, co- ${\mathbb Z}$-coverings, and circulations of –1, which transforms one automaton into the other. Moreover, the construction of these transformations is effective. This is obtained by combining two results: the first one relates coverings to conjugacy of automata, and is modeled after a theorem from symbolic dynamics; the second one is an adaptation of Schützenberger’s reduction algorithm of representations in a field to representations in an Euclidean domain (and thus in ${\mathbb Z}$).