On approximating real-world halting problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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The halting set K"@f={x|@f"x(x) converges}, for any Godel numbering @f={@f"0, @f"1,...}, is nonrecursive. It may be possible, however, to approximate K"@f by recursive sets. We note several results indicating that the degrees of recursive approximability of halting sets in arbitrary Godel numberings have wide variation, while restriction to ''optimal Godel numberings'' only narrows the possibilities slightly.