Sur une classe de transformations d'arbres
Représentations matricielles des séries d'arbre reconnaissables
On the syntactic complexity of tree series
We display a complexity notion based on the syntax of a tree series which yields two distinct hierarchies, one within the class of recognizable tree series and another one in the class of non-recognizable tree series.
Picture codes
We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set of pictures a picture code which is the basis of the least DR-monoid including . A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given.
Polypodic codes
Word and tree codes are studied in a common framework, that of polypodes which are sets endowed with a substitution like operation. Many examples are given and basic properties are examined. The code decomposition theorem is valid in this general setup.
Polypodic codes
Word and tree codes are studied in a common framework, that of polypodes which are sets endowed with a substitution like operation. Many examples are given and basic properties are examined. The code decomposition theorem is valid in this general setup.
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