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The halting problem is decidable on a set of asymptotic probability one

Joel David Hamkins·Alexei Miasnikov
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Abstract

The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n increases, the proportion of all n-state programs that are in B goes to one; (ii) B is polynomial time decidable; and (iii) the halting problem H intersect B is polynomial time decidable. The proof is sensitive to the particular computational model.

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Joel David Hamkins, Alexei Miasnikov. 2005-04-18. The halting problem is decidable on a set of asymptotic probability one. https://arxiv.org/abs/math/0504351

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