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I'm quite new to computability theory and would be interested in some examples of realistic programming tasks you could encounter when working as a C++ programmer that are not computable.

Graf Aal
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  • Are there some inputs that make my program crash?

  • Can this object be freed (from memory) or can it be needed later?

  • I'm building an editor and want to detect the programming language automatically. Given two languages described by CFGs, is there some input code for which I won't be able to guess the language (because it's valid in both languages)?

  • Do these two programs do the same thing?

Suppose that you have a property of programs so that:

  • It only depends on what the program does, not how it's written. So for example "It computes the factorial" or "It loops forever" work, but neither"It's written using a for loop" nor "It uses 5 variables" do.
  • There is some program that has the property
  • There is some program that doesn't have the property

Then Rice's theorem tells you that you can't have a (meta-)program that looks at source code and tells you if the program it describes has the property.

(My first and last examples are instances of that theorem)

xavierm02
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Another uncomputable function that would be useful is one that compresses any data into a shortest possible description of it.

Reinstate Monica
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