The halting problem for Turing machines is decidable on a set of asymptotic probability one. The proof is sensitive to the particular
computational models.
@article{1168352664,
author = {Hamkins, Joel David and Miasnikov, Alexei},
title = {The Halting Problem Is Decidable on a Set of Asymptotic Probability One},
journal = {Notre Dame J. Formal Logic},
volume = {47},
number = {1},
year = {2006},
pages = { 515-524},
language = {en},
url = {http://dml.mathdoc.fr/item/1168352664}
}
Hamkins, Joel David; Miasnikov, Alexei. The Halting Problem Is Decidable on a Set of Asymptotic Probability One. Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, pp. 515-524. http://gdmltest.u-ga.fr/item/1168352664/