Is finding the equivalence of two functions undecidable?

Question

Is it impossible to know if two functions are equivalent? For example, a compiler writer wants to determine if two functions that the developer has written perform the same

Answer 1

Note that the halting problem is decidable for linear bounded automata. Real computers are always bounded, and programs for them will always loop back to a previous configuration after sufficiently many steps. If you are using an unbounded (imaginary) computer to keep track of the configurations, you can detect that looping and take it into account.