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  • $\begingroup$ It may not be helpful to talk about programs. As soon as you have Turing-complete syntax/semantics, this property is not decidable by the theorem of Rice. You need weaker models of computation. Finite automata, for instance, have decidable equivalence, as do some flavors of Petri nets iirc. $\endgroup$ Commented Mar 9, 2016 at 12:23