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Communication Dans Un Congrès Année : 2005

On the equivalence of Z-automata

Résumé

We prove that two automata with multiplicity in Z are equivalent, i.e. define the same rational series, if and only if there is a sequence of Z-coverings, co-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 Z).

Dates et versions

hal-00017406 , version 1 (20-01-2006)

Identifiants

Citer

Marie-Pierre Béal, Sylvain Lombardy, Jacques Sakarovitch. On the equivalence of Z-automata. 2005, pp.397-409, ⟨10.1007/11523468_33⟩. ⟨hal-00017406⟩
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