Algebras, automata and logic for languages of labeled birooted trees

Abstract : In this paper, we study the languages of labeled finite birooted trees: Munn's birooted trees extended with vertex labeling. We define a notion of finite state birooted tree automata that is shown to capture the class of languages that are upward closed w.r.t. the natural order and definable in Monadic Second Order Logic. Then, relying on the inverse monoid structure of labeled birooted trees, we derive a notion of recognizable languages by means of (adequate) premorphisms into finite (adequately) ordered monoids. This notion is shown to capture finite boolean combinations of languages as above. We also provide a simple encoding of finite (mono-rooted) labeled trees in an antichain of labeled birooted trees that shows that classical regular languages of finite (mono-rooted) trees are also recognized by such premorphisms and finite ordered monoids.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [19 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00784898
Contributor : David Janin <>
Submitted on : Thursday, April 25, 2013 - 2:48:38 PM
Last modification on : Thursday, January 11, 2018 - 6:20:16 AM
Document(s) archivé(s) le : Friday, July 26, 2013 - 4:03:27 AM

File

RR1467-13.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

David Janin. Algebras, automata and logic for languages of labeled birooted trees. F. V. Fomin and M. Kwiatkowska and D. Peleg. ICALP, 2013, Riga, Latvia. Springer, 7966, pp.318-329, 2013, LNCS. 〈10.1007/978-3-642-39212-2_29〉. 〈hal-00784898v2〉

Share

Metrics

Record views

176

Files downloads

240