HAL : hal-00678190, version 1

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Paris : France (2012)

Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree

Antoine Durand-Gasselin, Peter Habermehl 1

(03/2012)

Many relational structures are automatically presentable, i.e. elements of the domain can be seen as words over a finite alphabet and equality and other atomic relations are represented with finite automata. The first-order theories over such structures are known to be primitive recursive, which is shown by the inductive construction of an automaton representing any relation definable in the first-order logic. We propose a general method based on Ehrenfeucht-Fraïssé games to give upper bounds on the size of these automata and on the time required to build them. We apply this method for two different automatic structures which have elementary decision procedures, Presburger Arithmetic and automatic structures of bounded degree. For the latter no upper bound on the size of the automata was known. We conclude that the very general and simple automata-based algorithm works well to decide the first-order theories over these structures.

1 :	Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA)
	CNRS : UMR7089 – Université Paris VII - Paris Diderot

Domaine

:

Informatique/Complexité Informatique/Algorithme et structure de données

Mots Clés : Automata-based decision procedures for logical theories – Automatic Structures – Ehrenfeucht-Fraïssé Games – Logics – Complexity

hal-00678190, version 1

http://hal.archives-ouvertes.fr/hal-00678190

oai:hal.archives-ouvertes.fr:hal-00678190

Contributeur : Christoph Dürr <>

Soumis le : Vendredi 3 Février 2012, 10:00:00

Dernière modification le : Lundi 12 Mars 2012, 10:45:01