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arXiv : 0901.3828

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International Journal of Foundations of Computer Science 15, 6 (2004) 823-840

On Recognizable Languages of Infinite Pictures

Olivier Finkel 1

(2004)

In a recent paper, Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Büchi and Muller ones, firstly used for infinite words. The authors asked for comparing the tiling system acceptance with an acceptance of pictures row by row using an automaton model over ordinal words of length $\omega^2$. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Büchi or Choueka automata reading words of length $\omega^2$ are Büchi recognized by a finite tiling system, but the converse is not true. We give also the answer to two other questions which were raised by Altenbernd, Thomas and Wöhrle, showing that it is undecidable whether a Büchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable).

1 :	Équipe de Logique Mathématique (ELM)
	CNRS : UMR7056 – Université Paris VII - Paris Diderot

Domaine

:

Informatique/Logique en informatique Informatique/Complexité Mathématiques/Logique

Mots Clés : Languages of infinite pictures – tiling systems – ordinal Büchi automaton – topological complexity – Borel and analytic sets – E-recognizable – A-recognizable – decision problems.

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Contributeur : Olivier Finkel <>

Soumis le : Samedi 24 Janvier 2009, 12:22:16

Dernière modification le : Samedi 24 Janvier 2009, 13:09:48