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Are there some undecidable problems for which there are efficient heuristic algorithms, that succeed on a sufficiently large subset of inputs to be worth using?

The one application that comes to mind is program static analysis: clearly undecidable (assuming infinite memory – I believe that it is PSPACE-complete if memory is finite but no practical algorithm I know of makes use of this, other than to bound the values of pointers), but in some cases it is possible to prove that a program satisfies a certain property.

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  • $\begingroup$ It sounds like you've answered your own question: yes, there are such problems, and you've given one example. What more are you looking for? It sounds like you're calling for a list of examples. We don't have a strict policy for list questions, but there is a general dislike. Also, there's no way anyone can compile a comprehensive list of all such examples, so I'm not seeing how this question is answerable in its current form. $\endgroup$ – D.W. Oct 2 '16 at 23:48
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    $\begingroup$ Termination and null pointer checking are two problems that even if undecidable seem to have been subject to lots of attention and heuristics in the literature $\endgroup$ – ejgallego Oct 3 '16 at 1:33
  • $\begingroup$ @DW I would like to know information about the general class of problems: Why do some undecidable problems have good heuristics, and others do not? $\endgroup$ – Demi Oct 4 '16 at 2:28

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