Abstract. Given a set of processes and a set of tests on these processes we show how to define in a natural way three different eyuitalences on processes. ThesP equivalences are applied to a particular language CCS. We give associated complete proof systems and fully abstract models. These models have a simple representation in terms of trees.

Two-thirds simulation is equivalent to failures refinement if two redundant transition rules are added to the operational semantics of CCS. This paper also shows how to define a process calculus in which the concepts of simulation and mutual refinement coincide with testing equivalence: thus the combined benefits of all three approaches are available uniformly to all applications. He Jifeng is a senior research-fellow of UNU/IIST. He is also a professor of computer science at the Software Engineering Institute of East China Normal University. His research interests include the theories of programming languages, formal methods for safety-critical systems, parallel and distributed systems, component-oriented computing, co-design techniques for real-time embedded systems. Email: jifeng@iist.unu.edu Professor Sir Tony Hoare held the James Martin Chair in Computing at the Oxford University Computing Laboratory from 1979 to 1999. Following his retirement from Oxford, he has taken up an appointment as Senior Researcher with Microsoft Research at Cambridge, where he is pursuing his long-term interest in programming theory. He is a fellow of the Royal Society of London. As one of the foremost experts in the field of computer science, he was knighted in 2000 for his achievements in software engineering. In further recognition of this, Sir Tony was awarded the Kyoto Prize for Advanced Technology in November 2000. Email: thoare@microsoft.com Copyright c fl 2003 by UNU/IIST, He Jifeng and Tony Hoare Contents i Contents 1