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Zbl 0689.68099
Bozapalidis, Symeon; Alexandrakis, Athanasios
Représentations matricielles des séries d'arbre reconnaissables. (Matrix representations of series on recognizable trees). (French)
[J] RAIRO, Inf. Théor. Appl. 23, No.4, 449-459 (1989). ISSN 0988-3754

We characterize recognizable formal series on trees by means of matrix representations. Further, we prove that the image of such a representation with minimum dimension is isomorphic to the syntactic ${\bbfK}-\Sigma$-algebra of the induced series. Finally, we show that two minimal matrix represenations of the same series, are ``similar''.

MSC 2000:: *68Q45 Formal languages
68Q70 Algebraic theory of automata
17A50 Nonassociative free algebras
08B20 Free algebras in varieties of algebras
05C05 Trees

Keywords: recognizable formal series on trees

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