The halting problem is decidable on a set of asymptotic probability one
Logic
2007-05-23 v1
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.
Cite
@article{arxiv.math/0504351,
title = {The halting problem is decidable on a set of asymptotic probability one},
author = {Joel David Hamkins and Alexei Miasnikov},
journal= {arXiv preprint arXiv:math/0504351},
year = {2007}
}
Comments
10 pages