Highly Undecidable Problems For Infinite Computations

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00349761
Contributeur : Olivier Finkel <>
Soumis le : dimanche 4 janvier 2009 - 12:10:13
Dernière modification le : vendredi 4 janvier 2019 - 17:32:32
Document(s) archivé(s) le : mardi 8 juin 2010 - 18:27:44

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  • HAL Id : hal-00349761, version 1
  • ARXIV : 0901.0373

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Olivier Finkel. Highly Undecidable Problems For Infinite Computations. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2009, 43 (2), pp.339-364. ⟨hal-00349761⟩

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