Abstract:
This note aims at bringing together the results of Castellani and Arnold-Dicky on characterizations of transition system equivalences by showing that observational equivalence can be characterized by saturating homomorphisms (with respect to Hennessy-Milner logic). We take this opportunity to compare Castellani's abstraction homomorphisms and Arnold-Dicky's saturating homomorphisms. It turns out that they are close but slightly different notions; this difference is partly due to the fact that abstraction homomorphisms were defined on a restricted class of transition systems.