• J. D. Hamkins and A. Miasnikov, “The halting problem is decidable on a set of asymptotic probability one,” Notre dame j. formal logic, vol. 47, iss. 4, pp. 515-524, 2006.  
  Journal MR Citation arχiv

  @ARTICLE{HamkinsMiasnikov2006:HaltingProblemDecidable,
  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},
  FJOURNAL = {Notre Dame Journal of Formal Logic},
  VOLUME = {47},
  YEAR = {2006},
  NUMBER = {4},
  PAGES = {515--524},
  ISSN = {0029-4527},
  CODEN = {NDJFAM},
  MRCLASS = {03D10 (68Q05)},
  MRNUMBER = {2272085 (2007m:03082)},
  MRREVIEWER = {Maurice Margenstern},
  DOI = {10.1305/ndjfl/1168352664},
  URL = {http://dx.doi.org/10.1305/ndjfl/1168352664},
  eprint = {math/0504351},
  file = F,
  }

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.