%0 Journal Article
%T Decision Problems For Turing Machines
%A Olivier Finkel
%A Dominique Lecomte
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0909.0736v1