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arXiv : 0901.0373

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RAIRO - Theoretical Informatics and Applications 43, 2 (2009) 339-364

Highly Undecidable Problems For Infinite Computations

Olivier Finkel 1, 2

(2009)

We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and ``highly undecidable". In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all $\Pi_2^1$-complete for context-free omega-languages or for infinitary rational relations. Topological and arithmetical properties of 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are also highly undecidable. These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite machines like 1-counter automata or 2-tape automata.

1 :	Équipe de Logique Mathématique (ELM)
	CNRS : UMR7056 – Université Paris VII - Paris Diderot
2 :	Laboratoire de l'Informatique du Parallélisme (LIP)
	Université de Lyon – CNRS : UMR5668 – INRIA – École Normale Supérieure - Lyon – Université Claude Bernard - Lyon I

Domaine

:

Informatique/Logique en informatique Informatique/Complexité Mathématiques/Logique

Mots Clés : Infinite computations – 1-counter-automata – 2-tape automata – decision problems – arithmetical hierarchy – analytical hierarchy – complete sets – highly undecidable problems.

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Contributeur : Olivier Finkel <>

Soumis le : Dimanche 4 Janvier 2009, 12:10:13

Dernière modification le : Mardi 4 Août 2009, 15:21:22