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| HAL : hal-00413331, version 1 |
| arXiv : 0909.0736 |
| Fiche détaillée |  Récupérer au format |
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| Information Processing Letters 109, 23-24 (2009) 1223-1226 |
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| Decision Problems For Turing Machines |
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| Olivier Finkel 1Dominique Lecomte 2 |
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| (2009) |
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| We answer two questions posed by Castro and Cucker, giving the exact complexities of two decision problems about cardinalities of omega-languages of Turing machines. Firstly, it is $D_2(\Sigma_1^1)$-complete to determine whether the omega-language of a given Turing machine is countably infinite, where $D_2(\Sigma_1^1)$ is the class of 2-differences of $\Sigma_1^1$-sets. Secondly, it is $\Sigma_1^1$-complete to determine whether the omega-language of a given Turing machine is uncountable. |
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| 1 : | Équipe de Logique Mathématique (ELM) |
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CNRS : UMR7056 – Université Paris VII - Paris Diderot |
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| 2 : | Institut de Mathématiques de Jussieu (IMJ) |
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CNRS : UMR7586 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| Domaine | : | Informatique/Logique en informatique Informatique/Complexité Mathématiques/Logique |
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| Theory of computation – computational complexity – formal languages – omega-languages – Turing machines – decision problems – analytical hierarchy. |
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| hal-00413331, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00413331 | |
| oai:hal.archives-ouvertes.fr:hal-00413331 | |
| Contributeur : Olivier Finkel | |
| Soumis le : Jeudi 3 Septembre 2009, 17:25:57 | |
| Dernière modification le : Jeudi 5 Novembre 2009, 17:37:20 | |
