On two mathematical definitions of observational equivalence: Manifest isomorphism and ε-congruence reconsidered

► Two proposed mathematical definitions of observational equivalence were examined. ► The first is Werndl's manifest isomorphism relation. ► The second is Ornstein and Weiss's epsilon congruence relation. ► Counterexamples demonstrate that neither definition is acceptable as stated. ► Prospects for a context-free definition of observational equivalence are dim.