The paper by R. De Nicola and M.C.B. Hennessy introduces a natural way to define three different equivalences on processes, which are applied to the process calculus language CCS. The authors provide associated complete proof systems and fully abstract models, which are represented in a simple tree structure. The first section formalizes the notion of equivalence between processes based on their behavior under a set of tests, considering the possibility of divergence. This leads to two preorders on processes: one based on the ability to respond positively to a test, and another on the inability not to respond positively. The natural equivalence is then obtained by combining these two preorders. The remainder of the paper focuses on applying these notions to CCS, specifying the set of processes, observers, states, and computations. It defines three different preorders on processes, corresponding to three powerdomain constructions, and derives three sound and complete proof systems for these relations. The paper also constructs fully abstract denotational models for CCS, showing that they can be represented as collections of trees. The final section relates the equivalences generated by the preorders to other research areas, such as observational equivalence, failures equivalence, and weak equivalence.The paper by R. De Nicola and M.C.B. Hennessy introduces a natural way to define three different equivalences on processes, which are applied to the process calculus language CCS. The authors provide associated complete proof systems and fully abstract models, which are represented in a simple tree structure. The first section formalizes the notion of equivalence between processes based on their behavior under a set of tests, considering the possibility of divergence. This leads to two preorders on processes: one based on the ability to respond positively to a test, and another on the inability not to respond positively. The natural equivalence is then obtained by combining these two preorders. The remainder of the paper focuses on applying these notions to CCS, specifying the set of processes, observers, states, and computations. It defines three different preorders on processes, corresponding to three powerdomain constructions, and derives three sound and complete proof systems for these relations. The paper also constructs fully abstract denotational models for CCS, showing that they can be represented as collections of trees. The final section relates the equivalences generated by the preorders to other research areas, such as observational equivalence, failures equivalence, and weak equivalence.