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arXiv : 0802.2866

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STACS 2008, Bordeaux : France (2008)

Cardinality and counting quantifiers on omega-automatic structures

Lukasz Kaiser 1, Sasha Rubin 2, Vince Bárány 1

(02/2008)

We investigate structures that can be represented by omega-automata, so called omega-automatic structures, and prove that relations defined over such structures in first-order logic expanded by the first-order quantifiers `there exist at most $\aleph_0$ many', 'there exist finitely many' and 'there exist $k$ modulo $m$ many' are omega-regular. The proof identifies certain algebraic properties of omega-semigroups. As a consequence an omega-regular equivalence relation of countable index has an omega-regular set of representatives. This implies Blumensath's conjecture that a countable structure with an $\omega$-automatic presentation can be represented using automata on finite words. This also complements a very recent result of Hjörth, Khoussainov, Montalban and Nies showing that there is an omega-automatic structure which has no injective presentation.

1 :	Mathematische Grundlagen der Informatik
	RWTH Aachen
2 :	Department of Computer Science [Auckland]
	The University of Auckland

Domaine

:

Informatique/Logique en informatique Informatique/Théorie de l'information et codage

Mots Clés : omega-automatic presentations – omega-semigroups – omega-automata

hal-00227560, version 1

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Contributeur : Pascal Weil <>

Soumis le : Jeudi 31 Janvier 2008, 05:32:09

Dernière modification le : Mercredi 20 Février 2008, 15:37:39