# A Combinatorial Theorem for Trees

1 GALION - Graphs, Automata, Logics, Languages and vErificatiON
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, UR1 - Université de Rennes 1, INSA Rennes - Institut National des Sciences Appliquées - Rennes, CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : Following the idea developped by I. Simon in his theorem of ramseyan factorisation forests, we develop a result of deterministic factorizations''. This extra determinism property makes it usable on trees (finite or infinite). We apply our result for proving that, \emph{over trees}, every monadic interpretation is equivalent to the composition of a first-order interpretation (with access to the ancestor relation) and a monadic marking. Using this remark, we give new caracterisations for prefix-recognisable structures and for the Caucal hierarchy. Furthermore, we believe that this approach has other potential applications.
Keywords :
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-00192024
Contributor : Thomas Colcombet Connect in order to contact the contributor
Submitted on : Monday, November 26, 2007 - 2:05:25 PM
Last modification on : Tuesday, June 15, 2021 - 4:04:13 PM

### Citation

Thomas Colcombet. A Combinatorial Theorem for Trees. ICALP, Jul 2007, Wroclaw, Poland. pp.901-912, ⟨10.1007/978-3-540-73420-8_77⟩. ⟨hal-00192024⟩

### Metrics

Les métriques sont temporairement indisponibles