 |
|
|
|
| HAL : hal-00373351, version 2 |
| Fiche détaillée |  Récupérer au format |
|
|
| 23rd International Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra : Portugal (2009) |
|
|
| Versions disponibles : | v1 (04-04-2009) | v2 (21-09-2009) |
|
|
|
|
| Linear Game Automata: Decidable Hierarchy Problems for Stripped-Down Alternating Tree Automata |
|
|
| Jacques Duparc 1Alessandro Facchini 2 |
|
|
| (07/09/2009) |
|
|
|
| For deterministic tree automata, classical hierarchies, like Mostowski-Rabin (or index) hierarchy, Borel hierarchy, or Wadge hierarchy, are known to be decidable. However, when it comes to non-deterministic tree automata, none of these hierarchies is even close to be understood. Here we make an attempt in paving the way towards a clear understanding of tree automata. We concentrate on the class of linear game automata (LGA), and prove within this new context, that all corresponding hierarchies mentioned above -Mostowski-Rabin, Borel, and Wadge - are decidable. The class LGA is obtained by taking linear tree automata with alternation restricted to the choice of path in the input tree. Despite their simplicity, LGA recognize sets of arbitrary high Borel rank. The actual richness of LGA is revealed by the height of their Wadge hierarchy: $({\omega^\omega})^\omega$. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut des systèmes d'information (ISI) |
|
|
|
Université de Lausanne |
|
|
| 2 : | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
|
|
|
CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunications de Bordeaux – Université Victor Segalen - Bordeaux II |
|
|
| 3 : | Laboratory for the Foundations of Computer Science [Edinburgh] (LFCS) |
|
|
|
University of Edinburgh |
|
|
|
|
|
|
|
|
|
| LaBRI |
|
|
|
|
| Domaine | : | Informatique/Logique en informatique |
|
|
| weak alternating tree automata – Wadge hierarchy – Index hierarchy – Borel hierarchy |
|
|
|
| Liste des fichiers attachés à ce document : | |||||
|
|||||
|
|
|
| hal-00373351, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00373351 | |
| oai:hal.archives-ouvertes.fr:hal-00373351 | |
| Contributeur : Alessandro Facchini | |
| Soumis le : Lundi 21 Septembre 2009, 12:37:38 | |
| Dernière modification le : Lundi 21 Septembre 2009, 14:55:12 | |
