Atomic Components

The operational definition of observational congruence in CCS and ACP can be split into two parts: one, the definition of an observational semantics (ie abstraction); and two, the definition of a strong congruence. In both cases this “separation of concerns” has been applied with abstraction that is implicitly “fair”. We define a novel (if obvious) observational semantics with no implicit “fairness”. When combining this observational semantics with failure equality the resulting observational semantics is shown to be equal, other than for minor details, to NDFD semantics. We also combine our observational semantics with singleton failure semantics and we establish congruence results for this new observational equality.