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arXiv : 0904.2894

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Mathematical Foundations of Computer Science 2009, Slovakia (2009)

On FO2 quantifier alternation over words

Manfred Kufleitner 1, Pascal Weil 2

ESF Program AutoMathA Collaboration(s)

(2009)

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels.

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 – Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunications de Bordeaux – Université Victor Segalen - Bordeaux II

Équipe de recherche : Méthodes Formelles

Domaine

:

Informatique/Logique en informatique

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Contributeur : Pascal Weil <>

Soumis le : Dimanche 19 Avril 2009, 04:36:56

Dernière modification le : Dimanche 5 Juillet 2009, 03:51:20