Sadly, even that is unprovable—I believe there’s a way to convert a solution for this problem to one for the halting problem.
Of course you can still do it for a large fraction of functions you’re likely to see in real life.
Yes—It’s not possible to decide, given two programs, if they have identical behavior. I think that’s okay here—the original poster asked for a definition of equivalence, not for a definition that was always decidable.
Sadly, even that is unprovable—I believe there’s a way to convert a solution for this problem to one for the halting problem.
Of course you can still do it for a large fraction of functions you’re likely to see in real life.
Yes—It’s not possible to decide, given two programs, if they have identical behavior. I think that’s okay here—the original poster asked for a definition of equivalence, not for a definition that was always decidable.