Examples
According to Rice's theorem, if there is at least one computable function in a particular class C of computable functions and another computable function not in C then the problem of deciding whether a particular program computes a function in C is undecidable. For example, Rice's theorem shows that each of the following sets of computable functions is undecidable:
- The class of computable functions that return 0 for every input, and its complement.
- The class of computable functions that return 0 for at least one input, and its complement.
- The class of computable functions that are constant, and its complement.
Read more about this topic: Rice's Theorem
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