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.Comment: To appear in Information Processing Letter

Dominique Lecomte

Equipe De Logique Mathématique

Olivier Finkel

English

arXiv

To appear in Information Processing Letters.International audienceWe 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

Finkel, Olivier

Lecomte, Dominique

Hal-Diderot

Decision Problems For Turing Machines

We answer two questions posed by Castro and Cucker in [CC89], giving the exact complexities of two decision problems about cardinalities of ω-languages of Turing machines. Firstly, it is D2(Σ 1 1)-complete to de-termine whether the ω-language of a given Turing machine is countably infinite, where D2(Σ 1 1) is the class of 2-differences of Σ

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Decision Problems For Turing Machines

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Hal-Diderot

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