HAL : hal-00567171, version 2

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Versions disponibles :

v1 (18-02-2011)

v2 (16-03-2012)

On logical hierarchies within FO2-definable languages

Manfred Kufleitner 1, Pascal Weil 2

(18/02/2011)

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose levels are varieties of languages (and hence admit an algebraic characterization). Using this algebraic approach, we show that the quantifier alternation hierarchy inside FO2[<] is decidable within one unit. For this purpose, we relate each level of the hierarchy with decidable varieties of languages, which can be defined in terms of iterated deterministic and co-deterministic products. A crucial notion in this process is that of condensed rankers, a refinement of the rankers of Weis and Immerman and the turtle languages of Schwentick, Therien and Vollmer.

1 :	Institut für Formale Methoden der Informatik
	Universität Stuttgart
2 :	Laboratoire Bordelais de Recherche en Informatique (LaBRI)
	CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II

Domaine

:

Informatique/Logique en informatique Informatique/Théorie et langage formel

hal-00567171, version 2

http://hal.archives-ouvertes.fr/hal-00567171

oai:hal.archives-ouvertes.fr:hal-00567171

Contributeur : Pascal Weil <>

Soumis le : Vendredi 16 Mars 2012, 10:02:54

Dernière modification le : Vendredi 16 Mars 2012, 16:58:36